alleryWhich of the following standard limits is equal to $1$?
A$\lim_{x\to 0}\dfrac{\sin x}{x}$
B$\lim_{x\to 0}\dfrac{\sin^2 x}{x}$
C$\lim_{x\to 0}\dfrac{\tan^2 x}{x}$
D$\lim_{x\to 0}\log_a(1+x)$
Answer & Solution
Correct answer: A. $\lim_{x\to 0}\dfrac{\sin x}{x}$
The standard trigonometric limit is $\lim_{x\to 0}\dfrac{\sin x}{x}=1$.
For B and C, since $\sin^2x\sim x^2$ and $\tan^2x\sim x^2$, dividing by $x$ gives a limit of $0$, not $1$.
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