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Webpage for Calculus:
Recent questions tagged calculus
2
votes
2
answers
1
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
in
Calculus
Feb 15
by
admin
819
views
gatecse-2023
calculus
maxima-minima
multiple-selects
1-mark
1
vote
2
answers
2
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)
admin
asked
in
Calculus
Feb 15
by
admin
798
views
gatecse-2023
calculus
definite-integral
numerical-answers
1-mark
0
votes
2
answers
3
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.
GO Classes
asked
in
Calculus
Feb 6
by
GO Classes
433
views
memorybased-gatecse2023
goclasses
calculus
maxima-minima
2
votes
1
answer
4
#Made Easy
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$
Dknights
asked
in
Calculus
Jan 31
by
Dknights
151
views
calculus
limits
1
vote
0
answers
5
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.
admin
asked
in
Calculus
Dec 15, 2022
by
admin
42
views
drdocse-2022-paper1
calculus
continuity-and-differentiability
5-marks
descriptive
0
votes
0
answers
6
Internet
For f(x)=√x x€[0,b] the number c satisfying mean value therom is c=1
Katyayani0306
asked
in
Calculus
Sep 21, 2022
by
Katyayani0306
123
views
continuity
calculus
0
votes
0
answers
7
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
Lakshman Patel RJIT
asked
in
Calculus
Sep 1, 2022
by
Lakshman Patel RJIT
139
views
tifr2022
calculus
maxima-minima
0
votes
0
answers
8
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 $c(t)$ ... $\frac{1}{2 \pi}$ $2 \pi$ $\sqrt{3} \pi$ $\frac{1}{\sqrt{3} \pi}$ $1$
Lakshman Patel RJIT
asked
in
Calculus
Sep 1, 2022
by
Lakshman Patel RJIT
119
views
tifr2022
calculus
differentiation
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