1
GATE CSE 2013
+1
-0.3
Function $$f$$ is known at the following points: The value of $$\int\limits_0^3 {f\left( x \right)dx}$$ computed using the trapezoidal rule is

A
$$8.983$$
B
$$9.003$$
C
$$9.017$$
D
$$9.045$$
2
GATE CSE 2013
+1
-0.3
Which one of the following functions is continuous at $$x=3?$$
A
$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$
B
$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$
C
$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$
D
$$f\left( x \right) = {1 \over {{x^3} - 27}},\,if\,\,x \ne 3$$
3
GATE CSE 2012
+1
-0.3
Consider the function $$f\left( x \right) = \sin \left( x \right)$$ in the interval $$x \in \left[ {\pi /4,\,\,7\pi /4} \right].$$ The number and location(s) of the local minima of this function are
A
One, at $$\pi /2$$
B
One, at $$3\pi /2$$
C
Two, at $$\pi /2$$ and $$3\pi /2$$
D
Two, at $$\pi /4$$ and $$3\pi /2$$
4
GATE CSE 2010
+1
-0.3
What is the value of $$\mathop {\lim }\limits_{n \to \infty } {\left[ {1 - {1 \over n}} \right]^{2n}}?$$
A
$$0$$
B
$${e^{ - 2}}$$
C
$${e^{ - 1/2}}$$
D
$$1$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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