Question

3. Evaluate the following limits: (16 pts) 3a) $\lim_{x \to 0^+} \left(\frac{3x+1}{x} - \frac{1}{\sin x}\right)$ 3b) $\lim_{x \to \frac{\pi}{2}} \frac{\ln(\csc x)}{(x-\frac{\pi}{2})^2}$ 3c) $\lim_{x \to e^+} (\ln x)^{\frac{1}{x-e}}$ 3d) $\lim_{x \to \infty} \left(\frac{3x-2}{3x+4}\right)^{2x+4}$

          3.
Evaluate the following limits: (16 pts)
3a) $\lim_{x \to 0^+} \left(\frac{3x+1}{x} - \frac{1}{\sin x}\right)$
3b) $\lim_{x \to \frac{\pi}{2}} \frac{\ln(\csc x)}{(x-\frac{\pi}{2})^2}$
3c) $\lim_{x \to e^+} (\ln x)^{\frac{1}{x-e}}$
3d) $\lim_{x \to \infty} \left(\frac{3x-2}{3x+4}\right)^{2x+4}$

3.
Evaluate the following limits: (16 pts)
3a) limx → 0^+((3x+1)/(x) - (1)/(sin x))
3b) limx →(π)/(2)(ln(csc x))/((x-(π)/(2))^2)
3c) limx → e^+ (ln x)^(1)/(x-e)
3d) limx →∞((3x-2)/(3x+4))^2x+4

Added by David P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/08/2022

Step 1

The limit of x sin x as x approaches 0 is of the form 0/0, so we can apply L'Hôpital's rule. Show more…

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