Calculus I - Week 04 Written HW

01

Finding limits - indeterminate form $\frac{0}{0}$ - absolute value denominator

Find the limit: $$\underset{x\to -6}{\lim }\frac{2x+12}{|x+6|}$$

Hint: translate the absolute value function into a description using cases.

Explicitly mention all limit laws that you use.

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02

Find limits at infinity

Find the limits:

• (a) $$\underset{x\to -\infty }{\lim }\frac{1-x^2}{x^3-x+1}$$
• (b) $$\underset{x\to +\infty }{\lim }\frac{x^4-3x^2+x}{x^3-x+2}$$

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03

Find limit at infinity - algebra tricks

Find the limit: $$\underset{x\to -\infty }{\lim }\frac{x}{\sqrt{x^2+1}}$$

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