Does L'H apply here?

Calculus Level 4

The graph of function y = f ( x ) y = f(x) has a unique tangent at ( e a , 0 ) (e^a,0) through which the graph passes, then lim ⁡ x → e a log ⁡ ( 1 + 7 f ( x ) ) − sin ⁡ ( f ( x ) ) 3 f ( x ) \displaystyle \lim_{x \to e^a} \cfrac{\log(1+7f(x)) - \sin (f(x))}{3f(x)} equals to

1 None of these 2 7

Kushashwa Ravi Shrimali by Kushashwa Ravi Shrimali , 22, India

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1 solution

Using L'hopital, we get : 7 1 + 7 f ( x ) − c o s ( f ( x ) ) 3 \frac{\frac{7}{1+7f(x)}-cos(f(x))}{3} As the derivative of f(x) cancels.

As f ( e a ) f(e^a) is zero , we get answer as 2 \boxed{2}

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