f(x) = (sin x)/x + cos x for x ≠ 0, and the value of f at x = 0 is k. For which k is f continuous at x = 0?

Continuity & Differentiability · Question 35 of 125

Question 35

EasyOriginal question

$f(x) = \frac{\sin x}{x} + \cos x$ for $x \ne 0$ , and the value of $f$ at $x = 0$ is $k$ . For which $k$ is $f$ continuous at $x = 0$ ?

0

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1

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2

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3

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CorrectNot quiteAnswer C

Correct answer: C

Worth noting

1 keeps only one of the two limits; each of $\frac{\sin x}{x}$ and $\cos x$ tends to 1.

Ten questions from Continuity & Differentiability, at your own pace.

Ten questions from Continuity & Differentiability, at your own pace.