Question

Determine values of $a$ and $b$ that make the given function continuous. $$f(x)=\left\{\begin{array}{ll} \frac{2 \sin x}{x} & \text { if } x<0 \\ a & \text { if } x=0 \\ b \cos x & \text { if } x>0 \end{array}\right.$$

          Determine values of $a$ and $b$ that make the given function continuous.
$$f(x)=\left\{\begin{array}{ll} \frac{2 \sin x}{x} & \text { if } x<0 \\ a & \text { if } x=0 \\ b \cos x & \text { if } x>0 \end{array}\right.$$

Added by Pamela G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Scott Stetson

Step 1

To do this, we need to find the limit of the function as $x$ approaches 0 from both the left and the right. From the left, we have $\lim_{x\to 0^-} \frac{2\sin x}{x} = 2$, since $\frac{\sin x}{x}$ approaches 1 as $x$ approaches 0. From the right, we have Show more…

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Determine values of $a$ and $b$ that make the given function continuous. $$f(x)=\left\{\begin{array}{ll} \frac{2 \sin x}{x} & \text { if } x<0 \\ a & \text { if } x=0 \\ b \cos x & \text { if } x>0 \end{array}\right.$$