Find the maximum and minimum values of f(x) = |x+3| ∀ \(x\in R\).

Find the point at which the curve y-e^xy+x=0 has a vertical tangent.

Using Rolle’s theorem find the value of c for f(x) = sin x in[0,2π]

Obtain Maclaurin’s Series expansion for e^2x.

Evaluate the following limits, if necessary using L’Hopitalrule
(i) \(\underset { x\rightarrow 2 }{ lim } \cfrac { sin\pi x }{ 2-x } \) 
(ii) \(\cfrac { lim }{ x\rightarrow 2 } \cfrac { { x }^{ n }-{ a }^{ n } }{ x-2 } \) 
(iii) \(\underset { x\rightarrow \infty }{ lim } \cfrac { sin\frac { 2 }{ x } }{ \frac { 1 }{ x } } \)
(iv) \(\underset { x\rightarrow \infty }{ lim } \cfrac { { x }^{ 2 } }{ { e }^{ x } } \)