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Webpage for Calculus:
Recent questions tagged calculus
3
votes
2
answers
61
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
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)| \...
admin
438
views
admin
asked
Mar 14, 2023
Calculus
tifr2023
calculus
continuity-and-differentiability
+
–
2
votes
1
answer
62
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
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 t...
admin
429
views
admin
asked
Mar 14, 2023
Calculus
tifr2023
calculus
functions
+
–
3
votes
1
answer
63
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.
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 $f^{\prime}(1)=0$. T...
admin
474
views
admin
asked
Mar 14, 2023
Calculus
tifr2023
calculus
differentiation
+
–
8
votes
2
answers
64
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.
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...
admin
5.1k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
maxima-minima
multiple-selects
1-mark
+
–
5
votes
2
answers
65
GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)
The value of the definite integral \[\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x\]is _________. (Rounde...
admin
8.5k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
definite-integral
numerical-answers
1-mark
+
–
0
votes
2
answers
66
GATE CSE 2023 | Memory Based Question: 11
Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE? $f(x)$ has a local maximum. $f(x)$ does NOT have a local maximum. $f(x)$ has a local minimum. $f(x)$ does NOT have a local minimum.
Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE?$f(x)$ has a local maximum.$f(x)$ does NOT have a local maximum.$f(x)$ has a local mi...
GO Classes
3.9k
views
GO Classes
asked
Feb 5, 2023
Calculus
memorybased-gatecse2023
goclasses
calculus
maxima-minima
+
–
3
votes
1
answer
67
#Made Easy
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$
Dknights
496
views
Dknights
asked
Jan 31, 2023
Calculus
calculus
limits
+
–
1
votes
1
answer
68
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.
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 th...
admin
329
views
admin
asked
Dec 15, 2022
Calculus
drdocse-2022-paper1
calculus
continuity-and-differentiability
5-marks
descriptive
+
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