1
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
$$f\left( x \right) = {1 \over {{x^3} - 27}},\,if\,\,x \ne 3$$
2
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 $$3\pi /2$$
3
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
$$1$$
4
GATE CSE 2008
+1
-0.3
$$\mathop {\lim }\limits_{x \to \infty } {{x - \sin x} \over {x + \cos \,x}}\,\,Equals$$
A
$$1$$
B
$$-1$$
C
$$\infty$$
D
$$- \infty$$
GATE CSE Subjects
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Medical
NEET