graph \( f(x)=x \cos x \) (a). \( \lim _{x \rightarrow 0} f(x) \) (b) \( \lim _{x-\pi / 3} \epsilon(x) \)

To find the limits of the function \( f(x) = x \cos x \) as \( x \) approaches 0 and as \( x \) approaches \( \frac{\pi}{3} \), we can use the following steps: (a) To find \( \lim_{x \rightarrow 0} f(x) \): We can directly substitute \( x = 0 \) into the function \( f(x) = x \cos x \) to find the limit. (b) To find \( \lim_{x \rightarrow \frac{\pi}{3}} f(x) \): We can directly substitute \( x = \frac{\pi}{3} \) into the function \( f(x) = x \cos x \) to find the limit. Let's calculate the limits. Evaluate the expression by following steps: - step0: Evaluate: \(xcosx\) - step1: Substitute: \(0\times cos\times 0\) - step2: Multiply the terms: \(0\times cos\) - step3: Multiply: \(0\times os\) - step4: Multiply: \(0\times s\) - step5: Multiply: \(0\) Substitute \( x = 0 \) into the function \( f(x) = x \cos x \) to find the limit as \( x \) approaches 0: \( \lim_{x \rightarrow 0} f(x) = 0 \) Now, let's calculate the limit as \( x \) approaches \( \frac{\pi}{3} \). Evaluate the expression by following steps: - step0: Evaluate: \(xcosx\) - step1: Substitute: \(\frac{\pi }{3}cos\left(\frac{\pi }{3}\right)\) - step2: Divide the terms: \(\frac{\pi }{3}cos\times \frac{\pi }{3}\) - step3: Multiply the terms: \(\frac{\pi ^{2}}{9}cos\) - step4: Multiply the terms: \(\frac{\pi ^{2}co}{9}s\) - step5: Multiply the terms: \(\frac{\pi ^{2}cos}{9}\) Substitute \( x = \frac{\pi}{3} \) into the function \( f(x) = x \cos x \) to find the limit as \( x \) approaches \( \frac{\pi}{3} \): \( \lim_{x \rightarrow \frac{\pi}{3}} f(x) = \frac{\pi}{6} \)