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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

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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

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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

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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

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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

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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

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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

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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

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