First slide

Introduction to limits

Question

The graph of y = f(x) has unique tangent at the point (a,0) through which the graph passes. Then $\lim_{x \to a} \frac{\log [1 + 6 f (x)]}{3 f (x)} =$

Moderate

A

0
B

1
C

2
D

$\infty$

Solution

$\lim_{x \to a} \frac{\log (1 + 6 f (x))}{3 f (x)} = \lim_{x \to a} \log (1 + 6 f {(x))}^{\frac{1}{3 f (x)}} = \log e^{2} = 2$

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