1
GATE CSE 2023
MCQ (More than One Correct Answer)
+1
-0

Let $$f(x) = {x^3} + 15{x^2} - 33x - 36$$ be a real-valued function. Which of the following statements is/are TRUE?

A
$$f(x)$$ does not have a local maximum.
B
$$f(x)$$ has a local maximum.
C
$$f(x)$$ does not have a local minimum.
D
$$f(x)$$ has a local minimum.
2
GATE CSE 2023
Numerical
+1
-0

The value of the definite integral

$$\int\limits_{ - 3}^3 {\int\limits_{ - 2}^2 {\int\limits_{ - 1}^1 {(4{x^2}y - {z^3})dz\,dy\,dx} } } $$

is ___________. (Rounded off to the nearest integer)

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3
GATE CSE 2022
Numerical
+1
-0

The value of the following limit is _____________.

$$\mathop {\lim }\limits_{x \to {0^ + }} {{\sqrt x } \over {1 - {e^{2\sqrt x }}}}$$

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4
GATE CSE 2021 Set 2
Numerical
+1
-0
Suppose that f : R → R is a continuous function on the interval [-3, 3] and a differentiable function in the interval (-3, 3) such that for every x in the interval, f'(x) ≤ 2. If f(-3) = 7, then f(3) is at most _______.
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GATE CSE Subjects
Software Engineering
Web Technologies
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