Calculus I - Week 01 Written HW

01

Compute difference quotient

Suppose $f(x)=-x^3$. Compute and simplify the difference quotient: $$\frac{f(a+h)-f(a)}{h}$$

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02

Domains of funny functions

Consider the following functions:

• (a) $f(x)=\sqrt{3-x}+\sqrt{4+x}$
• (b) $f(x)=\frac{x+1}{1+\frac{1}{1+x}}$

What is the largest possible domain for each of these functions?

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