Calculus I - Week 03 Written HW

03

Asymptotes

Find the vertical and horizontal asymptotes of this function: $$f(x)=\frac{x^2+1}{3x-2x^2}$$

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04

Confusing-but-not-hard limits

Find the following limits:

• (a) ${\lim }_{x\to {\pi }^{-}}x\cot x$
• (b) ${\lim }_{x\to 0^{+}}\left(\frac{1}{x}-\ln x\right)$
• (c) ${\lim }_{x\to 4}\frac{\ln x-\ln 4}{x-4}$ (for this one, first approximate with a calculator, then guess the exact answer)

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