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Recent questions and answers in Calculus
1
vote
2
answers
1
Evaluate the limit without using L' Hospital Rule.
Priyam Garg
answered
in
Calculus
Feb 28
by
Priyam Garg
233
views
limits
calculus
1
vote
2
answers
2
Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]
Sonu123x
answered
in
Calculus
Feb 28
by
Sonu123x
424
views
gate2024-da-memory-based
goclasses
calculus
limits
numerical-answers
2
votes
3
answers
3
ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then $f$ is not continuous at some points $f$ is continuous everywhere, but not differentiable anywhere $f$ is continuous everywhere, but not differentiable at exactly one point $f$ is differentiable everywhere
Sonu123x
answered
in
Calculus
Feb 24
by
Sonu123x
518
views
isi2016-mmamma
calculus
continuity
differentiation
0
votes
1
answer
4
ISI2016-MMA-24
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true? The limits $\lim_{x \rightarrow a+} f(x) $ and $\lim_{x \rightarrow a-} f(x)$ exist for all real numbers $a$ If $f$ is differentiable at $a$ then ... such that $f(x)<B$ for all real $x$ There cannot be any real number $L$ such that $f(x)>L$ for all real $x$
Sonu123x
answered
in
Calculus
Feb 24
by
Sonu123x
458
views
isi2016-mmamma
calculus
continuity
differentiation
limits
0
votes
2
answers
5
ISI2016-PCB-A-2
Let $n$ be a fixed positive integer. For any real number $x,$ if for some integer $q,$ $x=qn+r, \: \: \: 0 \leq r < n,$ then we define $x \text{ mod } n=r$. Specify the points of discontinuity of the function $f(x)=x \text{ mod } 3$ with proper reasoning.
Sonu123x
answered
in
Calculus
Feb 24
by
Sonu123x
405
views
isi2016-pcb-a
calculus
continuity
non-gate
descriptive
1
vote
4
answers
6
ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.
Sonu123x
answered
in
Calculus
Feb 23
by
Sonu123x
1.2k
views
isi2018-mma
engineering-mathematics
calculus
continuity
12
votes
4
answers
7
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
Priyam Garg
answered
in
Calculus
Feb 23
by
Priyam Garg
2.2k
views
tifr2011
calculus
limits
36
votes
2
answers
8
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
Sonu123x
answered
in
Calculus
Feb 23
by
Sonu123x
8.4k
views
gatecse-2008
calculus
maxima-minima
easy
0
votes
2
answers
9
ISI2015-DCG-57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one $y$ is not differentiable and many-one $y$ is not differentiable $y$ is differentiable and many-one
Sonu123x
answered
in
Calculus
Feb 22
by
Sonu123x
402
views
isi2015-dcg
calculus
continuity
differentiation
1
vote
3
answers
10
NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable
Sonu123x
answered
in
Calculus
Feb 22
by
Sonu123x
1.1k
views
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
15
votes
2
answers
11
GATE CSE 1987 | Question: 1-xxvi
If $f(x_{i}).f(x_{i+1})< 0$ then There must be a root of $f(x)$ between $x_i$ and $x_{i+1}$ There need not be a root of $f(x)$ between $x_{i}$ and $x_{i+1}$ There fourth derivative of $f(x)$ with respect to $x$ vanishes at $x_{i}$ The fourth derivative of $f(x)$ with respect to $x$ vanishes at $x_{i+1}$
Sonu123x
answered
in
Calculus
Feb 22
by
Sonu123x
2.7k
views
gate1987
calculus
maxima-minima
1
vote
2
answers
12
GATE CSE 2024 | Set 1 | Question: 1
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is $\{-1,1,2\}$ $\{-2,-1,1\}$ $\{0,1\}$ $\{-1,0,1\}$
phaniphani
answered
in
Calculus
Feb 17
by
phaniphani
3.2k
views
gatecse2024-set1
calculus
1
vote
1
answer
13
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \] Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \] ... Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
NarutoUzumaki
answered
in
Calculus
Feb 17
by
NarutoUzumaki
737
views
gate-ds-ai-2024
numerical-answers
limits
engineering-mathematics
4
votes
1
answer
14
GATE CSE 2024 | Set 2 | Question: 6
Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x)=1-f(2-x) \] Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ? $0$ $1$ $2$ $-1$
thehitchh1ker
answered
in
Calculus
Feb 17
by
thehitchh1ker
1.9k
views
gatecse2024-set2
calculus
definite-integral
1
vote
1
answer
15
DRDO CSE 2022 Paper 1 | Question: 4
Let the function $f(x)$ be defined as follows. \[f(x)=\left\{\begin{array}{ll} x^{2} & x \leq 1 \\ 2 a x^{2}+bx + c & 1 < x \leq 2 \\ x + 2d & x>1 \end{array}\right.\] Find the values of $a, b, c$ and $d$ such that $f$ is continuous and differentiable everywhere.
Lakshmi Narayana404
answered
in
Calculus
Feb 14
by
Lakshmi Narayana404
325
views
drdocse-2022-paper1
calculus
continuity-and-differentiability
5-marks
descriptive
6
votes
1
answer
16
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 10
Consider the following statements: $f(x)$ is continuous on $[a, b]$ $f(x)$ is differentiable on $(a, b)$ $f(a)=f(b)$ Which of the above statements are required in order to guarantee a $c \in(a, b)$ such that $f^{\prime}(c)(b-a)=f(b)-f(a) ?$ I only I and II only I, II, and III I and III only
Gouthamvu
answered
in
Calculus
Feb 8
by
Gouthamvu
497
views
goclasses2024-calculus-1
goclasses
calculus
continuity-differentiability
1-mark
0
votes
1
answer
17
Memory Based GATE DA 2024 | Question: 7
Consider the function \(f(x) = \frac{1}{1+e^{-x}}\). Determine the derivative \(f^{\prime}(x)\) when \(f(x) = 0.4\).
Lakshmi Narayana404
answered
in
Calculus
Feb 6
by
Lakshmi Narayana404
264
views
gate2024-da-memory-based
goclasses
calculus
maxima-minima
numerical-answers
0
votes
1
answer
18
Memory Based GATE DA 2024 | Question: 30
Consider the function \( F(x) \) defined as follows: \[ F(x) = \left\{ \begin{array}{cc} -x & \text{if } x < -2 \\ ax^2 + bx + c & \text{if } x \in [-2, 2] \\ x & \text{if } x > 2 \end{ ... \] \noindent Determine the values of \( a, b, \) and \( c \) such that \( F(x) \) is continuous and differentiable over its entire domain.
Lakshmi Narayana404
answered
in
Calculus
Feb 5
by
Lakshmi Narayana404
190
views
gate2024-da-memory-based
goclasses
calculus
continuity
1
vote
0
answers
19
Memory Based GATE DA 2024 | Question: 28
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) > 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f(X)\). \(X^*\) is a local maximum \(X^*\) is a local minimum \(X^*\) is a global maximum \(X^*\) is a global minimum
GO Classes
asked
in
Calculus
Feb 5
by
GO Classes
140
views
gate2024-da-memory-based
goclasses
calculus
maxima-minima
0
votes
0
answers
20
Memory Based GATE DA 2024 | Question: 52
Consider the function \(f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}\). Which of the following statements about the critical points of \(f(x)\) are correct? Local minima at \(x = 0\) Local maxima at \(x = 0\) Local minima at \(x = 3\) Local minima at \(x = -1\)
GO Classes
asked
in
Calculus
Feb 5
by
GO Classes
130
views
gate2024-da-memory-based
goclasses
calculus
maxima-minima
0
votes
2
answers
21
ISI2014-DCG-29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$ $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$ $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$ None of the above
Lakshmi Narayana404
answered
in
Calculus
Jan 31
by
Lakshmi Narayana404
693
views
isi2014-dcg
calculus
continuity
differentiation
2
votes
3
answers
22
ISI2014-DCG-17
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x-2}}}$ is $0$ $1/2$ $1$ non-existent
Lakshmi Narayana404
answered
in
Calculus
Jan 31
by
Lakshmi Narayana404
592
views
isi2014-dcg
calculus
limits
3
votes
2
answers
23
TIFR CSE 2023 | Part A | Question: 6
For a function $f: \mathbb{R} \rightarrow \mathbb{R},$ consider the following conditions. $\text{(C1)}$ $|f(x)| \leq|x|$ for all $x \in \mathbb{R}$. $\text{(C2)}$ $|f(x)| \leq|x|^{2}$ for all $x \in \mathbb{R}$. $\text{(C3)}$ ... $\text{(C3)}$ only Conditions $\text{(C1)}$ and $\text{(C2)}$ only Conditions $\text{(C2)}$ and $\text{(C3)}$ only
Lakshmi Narayana404
answered
in
Calculus
Jan 30
by
Lakshmi Narayana404
432
views
tifr2023
calculus
continuity-and-differentiability
26
votes
6
answers
24
GATE CSE 2015 Set 1 | Question: 4
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ $0$ $1$ Not defined
rajveer43
answered
in
Calculus
Jan 30
by
rajveer43
8.1k
views
gatecse-2015-set1
calculus
limits
normal
7
votes
2
answers
25
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 11
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivative $f^{\prime \prime}(x)$ changes sign at ... only inflection point. $x_0=0$ and $x_0=6$, both are inflection points. The function does not have an inflection point.
krishnajsw
answered
in
Calculus
Jan 29
by
krishnajsw
769
views
goclasses2024-mockgate-13
goclasses
calculus
maxima-minima
1-mark
14
votes
7
answers
26
GATE CSE 2019 | Question: 13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
gunaaaaa
answered
in
Calculus
Jan 26
by
gunaaaaa
6.2k
views
gatecse-2019
engineering-mathematics
calculus
limits
1-mark
0
votes
2
answers
27
ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
Lakshmi Narayana404
answered
in
Calculus
Jan 26
by
Lakshmi Narayana404
794
views
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
0
votes
1
answer
28
Thomas Calculus.
Consider the following statements, Statement 1:- $\lim_{x\to c}f(x) = L$ if and only if $\lim_{h \to 0 }f(h-c) = L$. Statement 2:- $\lim_{x\to c}f(x) = L$ if and only if $\lim_{h \to 0 }f(h+c) = L$ ... Statement 2 and Statement 4 are True. B. Statement 1 and Statement 3 are false. C. Statement 2 and Statement 3 are True. D. Statement 1 and Statement 4 are False.
Yati Maheshwari
answered
in
Calculus
Jan 24
by
Yati Maheshwari
165
views
calculus
limits
3
votes
2
answers
29
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 37
Which of the following is/are TRUE? There is a differentiable function $f(x)$ with the property that $f(1)=-2$ and $f(5)=14$ and $f^{\prime}(x)\lt 3$ for every real number $x$. There exists a function $f$ ... $a\lt c\lt b$ and $f(c)=0$. If $f$ is differentiable at the number $x$, then it is continuous at $x$.
Lakshmi Narayana404
answered
in
Calculus
Jan 21
by
Lakshmi Narayana404
588
views
goclasses2024-mockgate-12
goclasses
calculus
differentiation
multiple-selects
2-marks
3
votes
1
answer
30
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 31
If $f, f^{\prime}$, and $f^{\prime \prime}$ are continuous and $f(2)=0, f^{\prime}(2)=2$, and $f^{\prime \prime}(2)=-3$, what can we say about the function $f(x)$ at $x=2?$ $f$ has a local minimum at $x=2$. $f$ has a local maximum at $x=2$. $f$ is increasing, at $x=2$ $f$ is decreasing, at $x=2$
GO Classes
asked
in
Calculus
Jan 13
by
GO Classes
451
views
goclasses2024-mockgate-11
goclasses
calculus
maxima-minima
1-mark
0
votes
0
answers
31
GATE 2019 | MATHS | LIMIT
Let $ u_n = \frac{(n!)!}{1 \cdot 3 \cdot 5 \cdots (2n - 1)} $ (the set of all natural numbers). Then $ \lim\limits_{n \to \infty} \frac{n}{u_n} $ is equal to ______________
rajveer43
asked
in
Calculus
Jan 10
by
rajveer43
101
views
calculus
0
votes
0
answers
32
GATE 2022 | MATHS | Q-32
If the function \( f(x, y) = x^2 + xy + y^2 + \frac{1}{x} + \frac{1}{y} \), \( x \neq 0, y \neq 0 \), attains its local minimum value at the point \((a, b)\), then the value of \(a^3 + b^3\) is _________(rounded off to TWO decimal places).
rajveer43
asked
in
Calculus
Jan 10
by
rajveer43
70
views
calculus
0
votes
0
answers
33
Thomas Calculus
Prove that $\lim_{x->5} \frac{1}{x-3} = \frac{1}{2}$, using Epsilon Delta Definition.
Lakshmi Narayana404
asked
in
Calculus
Jan 10
by
Lakshmi Narayana404
52
views
limits
calculus
0
votes
1
answer
34
Rolle's Mean Value Theorem
Debargha Mitra Roy
asked
in
Calculus
Dec 1, 2023
by
Debargha Mitra Roy
168
views
calculus
0
votes
1
answer
35
Limit
Debargha Mitra Roy
asked
in
Calculus
Nov 26, 2023
by
Debargha Mitra Roy
128
views
limits
calculus
1
vote
1
answer
36
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 5
$\lim _{x \rightarrow 2} \frac{\sqrt{x}-\sqrt{2}}{x-2}$ $0$ $\sqrt{2}$ $\frac{1}{2 \sqrt{2}}$ $\frac{1}{\sqrt{2}}$
admin
asked
in
Calculus
Oct 22, 2023
by
admin
766
views
gateda-sample-paper-2024
limits
0
votes
0
answers
37
Made Easy Test Series 2024
please anyone explain this question .?
Ray Tomlinson
asked
in
Calculus
Oct 12, 2023
by
Ray Tomlinson
341
views
made-easy-test-series
made-easy-booklet
calculus
linear-algebra
made-easy-test-series-2024
2
votes
1
answer
38
TIFR CSE 2023 | Part A | Question: 7
Suppose $f(x)$ is a polynomial of the form $a x^{2}+b x+c,$ with $a, b, c$ unknown real numbers. Suppose you are additionally told that $f(1)=2$ and $f(-1)=3$. Consider the following four statements. $\text{(S1)}$ $f(0)$ cannot be ... $\text{(S4)}$ only Statement $\text{(S3)}$ only Statements $\text{(S3)}$ and $\text{(S4)}$ only All four statements are true
admin
asked
in
Calculus
Mar 14, 2023
by
admin
421
views
tifr2023
calculus
functions
3
votes
1
answer
39
TIFR CSE 2023 | Part A | Question: 14
Let $f(x)=a x^{3}+b x^{2}+c x+d$ be a polynomial, where $a, b, c, d$ are unknown real numbers. It is further given that $f(1)=1, f(2)=2, f(3)=9$, and $f^{\prime}(1)=0$. Then, the value of $f^{\prime}(2)$ must be $1$ $2$ $3$ $4$ $f^{\prime}(2)$ cannot be determined uniquely from the information given in the question.
admin
asked
in
Calculus
Mar 14, 2023
by
admin
472
views
tifr2023
calculus
differentiation
8
votes
2
answers
40
GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.
admin
asked
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Calculus
Feb 15, 2023
by
admin
5.1k
views
gatecse-2023
calculus
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