GATE CSE 2013 | Calculus Question 30 | Discrete Mathematics

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which one of the following functions is continuous at $$x=3?$$

$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$

$$f\left( x \right) = {1 \over {{x^3} - 27}},\,if\,\,x \ne 3$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Function $$f$$ is known at the following points: GATE CSE 2013 Discrete Mathematics - Calculus Question 32 English

The value of $$\int\limits_0^3 {f\left( x \right)dx} $$ computed using the trapezoidal rule is

$$8.983$$

$$9.003$$

$$9.017$$

$$9.045$$

GATE CSE 2012

MCQ (Single Correct Answer)

-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

One, at $$\pi /2$$

One, at $$3\pi /2$$

Two, at $$\pi /2$$ and $$3\pi /2$$

Two, at $$\pi /4$$ and $$3\pi /2$$

GATE CSE 2010

MCQ (Single Correct Answer)

-0.3

What is the value of $$\mathop {\lim }\limits_{n \to \infty } {\left[ {1 - {1 \over n}} \right]^{2n}}?$$

$$0$$

$${e^{ - 2}}$$

$${e^{ - 1/2}}$$

$$1$$