\(\lim _{ x\rightarrow \infty }{ \left( \frac { 1 }{ x } +2 \right) } \)is equal to

(a)

\(\infty \)

(b)

0

(c)

1

(d)

2

If y= 6x -x³ and x increases at the ratio of 5 units per second, the rate of change of slope when x = 3 is ______ units/sec.

(a)

-90

(b)

90

(c)

180

(d)

-180

The slope of the graph of \(f\left( x \right) =\frac { \left| x \right| }{ x } ,x>0\quad is\)

(a)

1

(b)

0

(c)

-1

(d)

undefined

Choose the incorrect pair

(a)

\(\underset { x\rightarrow \infty }{ lim } \frac { sin\quad x }{ x } =0\)

(b)

\(\underset { x\rightarrow \frac { \pi }{ 2 } }{ lim } \frac { 2x-\pi }{ cos\quad x } =-2\)

(c)

\(\underset { x\rightarrow \infty }{ lim } \frac { { a }^{ x }-{ b }^{ x } }{ x } =log\left( \frac { a }{ b } \right) \)

(d)

\(\frac { { a }^{ x }-1 }{ x } =log\ a>0\)

Choose the incorrect statement

(a)

log 1 to any base is zero

(b)

\(\frac{d}{dx}\) (e^x)=e^x

(c)

Inverse function of log x is \(\frac{1}{x}\)

(d)

|x| is not differentiable at x =0