Evaluate the limits \(\lim _{ x\rightarrow 3 }{ { (4x }^{ 3 }-{ 2x }^{ 2 } } -x+1)\)

3

(a)

Find the value of \(\lim _{x \rightarrow 0} \frac{e^{3 x}-1}{x}\)

3

(a)

Evaluate \(\lim _{x \rightarrow \pi / 2} \frac{1+\cos 2 x}{(\pi-2 x)^{2}}\)

3

(a)

Find the derivative of a^x from first principle.

3

(a)

Evaluate  \(\lim _{x \rightarrow \frac{1}{2}} \frac{4 x^{2}-1}{2 x-1}\)

3

(a)

If u = 7t⁴ - 2t³ - 8t - 5, then find \(\frac { du }{ dt } \) at t = 2

3

(a)

Evaluate \(\lim _{x \rightarrow 2} \frac{x^{2}-x \log x+2 \log x-4}{x-2}\)

3

(a)

Evaluate \(\lim _{x \rightarrow 2}\left[\frac{x^{2}-4}{x^{3}-4 x^{2}+4 x}\right]\)

3

(a)

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

3

(a)

Evaluate the following limits \(\lim _{x \rightarrow 0} \frac{\log (5+x)-\log (5-x)}{x}\)

3

(a)

Evaluate the following limits \(\lim _{x \rightarrow 0} \frac{a^{x}-b^{x}}{\sin x}\)

3

(a)

Evaluate: \(\underset { x\rightarrow o }{ Lim } \frac { { e }^{ tanx }-1 }{ log(1+x) } \)

3

(a)

Evaluate:\(\lim_ { x\rightarrow o } \frac { { e }^{ { x }^{ 2 } }-cosx }{ { x }^{ 2 } } \)

3

(a)

Evaluate: \(\lim_{x\rightarrow 0} \frac{x(e^{x}-1)}{1-cos x}\)

3

(a)

Evaluate: \(\lim_{x\rightarrow 0} \frac{log_{e} (1+2x)}{x}\)

3

(a)