If \(f(x)=\left\{\begin{array}{ll} |x|+1, & x<0 \\ 0, & x=0 \\ |x|-1, & x>0 \end{array}\right.\)for what values of a does \(\overset{lim}{x\rightarrow a}\)f(x) exists?

5

(a)

Find the derivative of the following functions from first principle:
(i) - x
(ii) (- x)^-1
(iii) sin (x +1)
(iv) \(\cos\left( x-\frac { \pi }{ 8 } \right) \)

5

(a)

Find the derivative of (x+a) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

5

(a)

Find the derivative of  \((px+q)\left( \frac { r }{ x } +s \right) \) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

5

(a)

Find the derivative of \(\frac { ax+b }{ cx+d } \) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

5

(a)

Find the derivative of \(\frac { 1 }{ { ax }^{ 2 }+bx+c } \) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

5

(a)

Find the derivative of \(\frac { { (px }^{ 2 }+qx+r) }{ ax+b } \) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

5

(a)

Evaluate:\(\underset { x\rightarrow o }{ Lim } \frac { { 27 }^{ x }-{ 9 }^{ x }-{ 3 }^{ x }+1 }{ 1-cosx } \)

5

(a)

Find the derivative of  \(\frac { a+b\sin\ x }{ c+d \cos\ x } \) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

5

(a)

Differentiate cot\(\sqrt{x}\) w.r.t. x from first principle method.

5

(a)

Evaluate: \(\overset{Lt}{x\rightarrow e}\frac{log x-1}{x-e}\)

5

(a)

Evaluate: \(\overset{Lt}{x\rightarrow 0} [tan(\frac{\pi}{4}+x)]^{\frac{1}{cotx}}\)

5

(a)