Question

Using L’Hospital’s Rule, evaluate: lim_{x → 0} ( 1 + sin x )^{cot x}

Answer 1

`Lim_( x → 0) (1+sin x)^(cot x) = Lim_( x → 0 ) e^(sin x cot x)`

= `Lim_(x → 0 ) e^  ("sin"x". cos"x" )/(sin x)`

= `lim_(x → 0 )e^ cos x `

= e ^{cos 0}          

= e.