Question:
$\displaystyle\lim_{x\to0} \frac{\sin x}{x}$ is equal to
$\displaystyle\lim_{x\to0} \frac{\sin x}{x}$ is equal to
Updated On: Jun 17, 2022
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The Correct Option is C
Solution and Explanation
$\displaystyle\lim _{x \rightarrow 0} \frac{\sin x}{x}=\displaystyle\lim _{x \rightarrow 0} \frac{\cos x}{1}$
$=\cos 0=1$
$=\cos 0=1$
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Concepts Used:
Limits of Trigonometric Functions
Assume a is any number in the general domain of the corresponding trigonometric function, then we can explain the following limits.
We know that the graphs of the functions y = sin x and y = cos x detain distinct values between -1 and 1 as represented in the above figure. Thus, the function is swinging between the values, so it will be impossible for us to obtain the limit of y = sin x and y = cos x as x tends to ±∞. Hence, the limits of all six trigonometric functions when x tends to ±∞ are tabulated below:
