Question

Evaluate Limit x -> a x sina - asinx / x - a

Answer 1

let l=lim(x->a) (xsina - asinx) / (x-a) 
this is of form 0/0...............substituting x=a 

therefore, we can apply L' Hospital's Rule; so differentiating numerator and denominator respectively. 

=>l= lim(x->a) (sina - acosx)/1 
=>l=sina - acosa 
which is the required limit.

Answer 2

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