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Recent questions tagged calculus
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For f(x)=√x x€[0,b] the number c satisfying mean value therom is c=1
For f(x)=√x x€[0,b] the number c satisfying mean value therom is c=1
Katyayani0306
234
views
Katyayani0306
asked
Sep 21, 2022
Calculus
continuity
calculus
+
–
0
votes
2
answers
92
TIFR CSE 2022 | Part A | Question: 6
Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)?$ $1$ $n$ $n+1$ $\frac{n(n+1)}{2}$ $f^{\prime}(1)$ can be arbitrarily large given only the constraints in the question
Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)...
admin
669
views
admin
asked
Sep 1, 2022
Calculus
tifr2022
calculus
maxima-minima
+
–
0
votes
0
answers
93
TIFR CSE 2022 | Part A | Question: 14
Suppose $w(t)=4 e^{i t}, x(t)=3 e^{i(t+\pi / 3)}, y(t)=3 e^{i(t-\pi / 3)}$ and $z(t)=3 e^{i(t+\pi)}$ are points that move in the complex plane as the time $t$ varies in $(-\infty, \infty)$. Let $c(t)$ ... $\frac{1}{2 \pi}$ $2 \pi$ $\sqrt{3} \pi$ $\frac{1}{\sqrt{3} \pi}$ $1$
Suppose $w(t)=4 e^{i t}, x(t)=3 e^{i(t+\pi / 3)}, y(t)=3 e^{i(t-\pi / 3)}$ and $z(t)=3 e^{i(t+\pi)}$ are points that move in the complex plane as the time $t$ varies in $...
admin
319
views
admin
asked
Sep 1, 2022
Calculus
tifr2022
calculus
differentiation
+
–
1
votes
2
answers
94
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 1
Evaluate the limit $ \lim _{x \rightarrow 0} \frac{1-\cos x}{\sin ^{2} x} $ $1$ $\frac{1}{2}$ $2$ $0$
Evaluate the limit$$\lim _{x \rightarrow 0} \frac{1-\cos x}{\sin ^{2} x}$$$1$$\frac{1}{2}$$2$$0$
GO Classes
663
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
limits
1-mark
+
–
3
votes
1
answer
95
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 2
Determine the value of following limit $ \lim _{x \rightarrow \infty}\left(\sqrt{x^{2}+4 x+1}-x\right) $ $2$ $4$ $\frac{1}{2}$ $3$
Determine the value of following limit$$\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}+4 x+1}-x\right)$$$2$$4$$\frac{1}{2}$$3$
GO Classes
573
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
limits
1-mark
+
–
3
votes
3
answers
96
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 3
The function $f(x)=x^{4}-6 x^{2}$ is increasing on the intervals $(0, \sqrt{3})$ only $(\sqrt{3}, \infty)$ only $(-\infty,-\sqrt{3})$ and $(0, \sqrt{3})$ only $(-\sqrt{3}, 0)$ and $(\sqrt{3}, \infty)$ only
The function $f(x)=x^{4}-6 x^{2}$ is increasing on the intervals$(0, \sqrt{3})$ only$(\sqrt{3}, \infty)$ only$(-\infty,-\sqrt{3})$ and $(0, \sqrt{3})$ only$(-\sqrt{3}, 0)...
GO Classes
605
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
maxima-minima
1-mark
+
–
5
votes
1
answer
97
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 4
The function $f(x)=\cos x-x$ is an even function is an odd function is neither an even nor an odd function None of these
The function $f(x)=\cos x-x$is an even functionis an odd functionis neither an even nor an odd functionNone of these
GO Classes
446
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
functions
1-mark
+
–
8
votes
2
answers
98
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 5
Which of the following functions satisfy the conditions of Rolle's Theorem on the interval $[-1,1]?$ $ \begin{aligned} &f(x)=1-x^{2 / 3}\\ &g(x)=x^{3}-2 x^{2}-x+2\\ &h(x)=\cos \left(\frac{\pi}{4}(x+1)\right) \end{aligned} $ Rolle's Theorem applies to: both $f$ and $g$ both $g$ and $h$ $g$ only $h$ only
Which of the following functions satisfy the conditions of Rolle's Theorem on the interval $[-1,1]?$ $$\begin{aligned}&f(x)=1-x^{2 / 3}\\&g(x)=x^{3}-2 x^{2}-x+2\\&h(x)=\c...
GO Classes
977
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
1-mark
+
–
4
votes
1
answer
99
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 6
Suppose that the derivative of a function $h$ is given by: $ h^{\prime}(x)=x(x-1)^{2}(x-2) $ On what interval(s) is $h$ increasing? $(-\infty, 0)$ $(-\infty, 0)$ and $(2, \infty)$ $(0,2)$ $(0,1)$ and $(2, \infty)$
Suppose that the derivative of a function $h$ is given by:$$h^{\prime}(x)=x(x-1)^{2}(x-2)$$On what interval(s) is $h$ increasing?$(-\infty, 0)$$(-\infty, 0)$ and $(2, \in...
GO Classes
547
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
1-mark
+
–
7
votes
3
answers
100
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 7
Let $q(x)$ be a continuous function which is defined for all real numbers. A portion of the graph of $q^{\prime}(x)$, the derivative of $q(x)$, is shown below. On which of the following interval(s) is $q(x)$ increasing? $(0,2)$ $(2,4)$ $(7,9)$ None of these
Let $q(x)$ be a continuous function which is defined for all real numbers. A portion of the graph of $q^{\prime}(x)$, the derivative of $q(x)$, is shown below.On which of...
GO Classes
779
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
multiple-selects
1-mark
+
–
7
votes
2
answers
101
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 8
Choose the CORRECT statement - The function $f(x)=\exp \left(-x^{2}\right)-1$ has the root $x=0$. If a function $f$ is differentiable on $[-1,1]$, then there is a point $x$ in that interval where $f^{\prime}(x)=0$. If $1$ is a ... at $1 .$ If $f^{\prime \prime}(0)0$ then there is a point in $(0,1)$, where $f$ has an inflection point.
Choose the CORRECT statement -The function $f(x)=\exp \left(-x^{2}\right)-1$ has the root $x=0$.If a function $f$ is differentiable on $[-1,1]$, then there is a point $x$...
GO Classes
897
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
multiple-selects
1-mark
+
–
3
votes
1
answer
102
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 9
Evaluate $y^{\prime \prime}(1)$ where $y=e^{x}+x^{e}$. $0$ $1$ $e^{2}$ $e$
Evaluate $y^{\prime \prime}(1)$ where $y=e^{x}+x^{e}$.$0$$1$$e^{2}$$e$
GO Classes
399
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
1-mark
+
–
6
votes
1
answer
103
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 10
Consider the following statements: $f(x)$ is continuous on $[a, b]$ $f(x)$ is differentiable on $(a, b)$ $f(a)=f(b)$ Which of the above statements are required in order to guarantee a $c \in(a, b)$ such that $f^{\prime}(c)(b-a)=f(b)-f(a) ?$ I only I and II only I, II, and III I and III only
Consider the following statements:$f(x)$ is continuous on $[a, b]$$f(x)$ is differentiable on $(a, b)$$f(a)=f(b)$Which of the above statements are required in order to gu...
GO Classes
512
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
continuity-differentiability
1-mark
+
–
7
votes
1
answer
104
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 11
Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements - If $f^{\prime}(x)=0$ for all $x \in I$, then there is a constant $r$ such that $f(x)=r$ ... decreasing on $I$. If $f^{\prime}(x)>0$ for all $x \in I$, then $f(x)$ is strictly decreasing on $I$.
Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements -If $f^{\prime}(x)=0$ for all ...
GO Classes
546
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
+
–
8
votes
1
answer
105
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 12
Which of the following is/are FALSE? The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$ If $f(x)$ is a continuous function and $f(3)=2$ and $f(5)=-1$, then $f(x)$ has a root between $3$ and $5 .$ ... $h(x)$ is a continuous function and $h(1)=4$ and $h(2)=5$, then $h(x)$ has no roots between $1$ and $2.$
Which of the following is/are FALSE?The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$If $f(x)$ is a continuous function and $f(3)=2$ and $...
GO Classes
564
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
+
–
6
votes
1
answer
106
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 13
Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that $g(c)=1$ $g^{\prime}(c)=1$ $g(c)=0$ $g^{\prime}(c)=0$
Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that$g(c)=1$$g^{\prime}(c)=1$$g(c)=0$$g^{\p...
GO Classes
617
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
2
votes
2
answers
107
GO Classes Test Series 2023 | Calculus | Test | Question: 14
Which of the following limit is/are correct? $\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=1$ $\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=e$ $\displaystyle{}\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{x}=e^{2}$ $\displaystyle{}\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{x}=e$
Which of the following limit is/are correct?$\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=1$$\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=e$$\displa...
GO Classes
454
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
limits
multiple-selects
2-marks
+
–
6
votes
1
answer
108
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 15
Suppose $f$ is twice differentiable with $ f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 . $ Find $f(0)$. $-337 / 6$ $-74 / 3$ $23 / 9$ $37 / 4$
Suppose $f$ is twice differentiable with$$f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 .$$Find $f(0)$.$-337 / 6$$-74 / 3$$23 / 9...
GO Classes
519
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
2-marks
+
–
4
votes
1
answer
109
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 16
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product. $86$ $64$ $48$ $72$
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product.$86$$64$$48$$72$
GO Classes
475
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
3
votes
2
answers
110
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 17
If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is $1$ $3$ $2$ $0$
If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is$1$$3$$2$$0$
GO Classes
344
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
6
votes
1
answer
111
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 18
Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then $f(6) \geq 8$ $f(6)<8$ $f(6)<5$ $f(6)=5$
Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then$f(6) \geq 8$$f(6)<8$$f(6)<5$$f(6)=5$
GO Classes
427
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
8
votes
1
answer
112
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 19
The equation $x^{5}+x+1=0$ has a solution in the interval $[0,1]$ $[-1,0]$ $[-2,-1]$ $[1,2]$
The equation $x^{5}+x+1=0$ has a solution in the interval$[0,1]$$[-1,0]$$[-2,-1]$$[1,2]$
GO Classes
507
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
2
votes
1
answer
113
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 20
Which of the following expression evaluates to given integral $ \int \frac{\ln (\ln x)}{x \ln x} d x $ $\dfrac{\ln x}{x}+C$ $\frac{1}{2}(\ln \ln x)^{2}+C$ $(\ln x)^{2}+C$ $(\ln \ln x)+C$
Which of the following expression evaluates to given integral$$\int \frac{\ln (\ln x)}{x \ln x} d x$$$\dfrac{\ln x}{x}+C$$\frac{1}{2}(\ln \ln x)^{2}+C$$(\ln x)^{2}+C$$(\l...
GO Classes
509
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
integration
2-marks
+
–
1
votes
0
answers
114
Engineering Mathematics
Please verify the solution(the differentiation part ),
Please verify the solution(the differentiation part ),
Overflow04
564
views
Overflow04
asked
Aug 21, 2022
Calculus
calculus
ace-test-series
+
–
0
votes
1
answer
115
Maths for natural science
Determine the domain of the function $f(x)=\left | x \right |+1$
Determine the domain of the function $f(x)=\left | x \right |+1$
Hailemariam
301
views
Hailemariam
asked
Aug 5, 2022
Calculus
calculus
functions
+
–
0
votes
0
answers
116
mathematics for natural science
Suppose a radioactive substance decays according to the equation $y=2000e^{-0.75t}$, where $y$ represent the mass in grams after $t$ hours. Assume that the half-life of radium is $1600$ years. If $y_{0}$ milligrams of radium are initially present, write the formula for the number of milligrams $y$ present after $t$ years.
Suppose a radioactive substance decays according to the equation $y=2000e^{-0.75t}$, where $y$ represent the mass in grams after $t$ hours.Assume that the half-life of r...
Hailemariam
374
views
Hailemariam
asked
Aug 4, 2022
Others
calculus
+
–
0
votes
1
answer
117
Mathematics for Natural Science
Determine the domain of the function $f(x) = |x – 2|$
Determine the domain of the function $f(x) = |x – 2|$
Hailemariam
235
views
Hailemariam
asked
Aug 3, 2022
Calculus
calculus
+
–
0
votes
0
answers
118
Mathematics for Natural Science
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$
kidussss
366
views
kidussss
asked
Jul 29, 2022
Calculus
calculus
+
–
0
votes
0
answers
119
Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
kidussss
315
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
0
votes
1
answer
120
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
kidussss
234
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
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