If \(f(x)=\left\{\begin{array}{l} x+2, x \leq-1 \\ c x^{2}, x>-1 \end{array}\right.\) then find c when \(\lim _{ x\rightarrow -1 }{ f(x) } \) exists.

2

(a)

Show that \(\lim _{ x\rightarrow 4 }{ \frac { |x-4| }{ x-4 } } \)does not exist.

2

(a)

Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{\sqrt{3} \sin x-\cos x}{x-\frac{\pi}{6}}\)

2

(a)

Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}\) by using factorization method

2

(a)

Find the derivative of the following functions,
\(\frac { sinx+cosx }{ sinx-cosx } \)
First, consider the given function as f(x). Then, use quotient rule to find the required derivative.

2

(a)

Evaluate \(\lim_ { x\rightarrow \pi /2 }{ lim } \left( sec \ x-tan \ x \right) .\)

2

(a)

Differentiate the function \(\cos { \left( { x }^{ 2 }+1 \right) } \) by the first principle.

2

(a)

Find the derivative of the following functions, \(\frac { secx+tanx }{ secx-tanx } \) First, consider the given function as f(x). Then, use quotient rule to find the required derivative.

2

(a)

Find the derivates of the following function by using first principle.
sec x

2

(a)

Find the derivates of the following function by using first principle.
tan x

2

(a)