91Ó°ÊÓ

Evaluate the limits that exist. $$\lim _{h \rightarrow 0} h\left(1+\frac{1}{h}\right)$$

Decide in the manner of Section 2.1 whether or not the indicated limit exists. Evaluate the limits that do exist. $$\lim _{x \rightarrow 2} f(x) \text { if } f(x)=\left\\{\begin{array}{ll} 3 . & x \text { an integer } \\ 1 . & \text { otherwise } \end{array}\right.$$

Sketch the graph and classify the discontinuities (if any) as being removable or essential. If the latter, is it a jump discontinuity, an infinite discontinuity, or neither. $$f(x)=|x-1|$$.

Decide on intuitive grounds whether or not the indicated limit exists; evaluate the limit if it does exist. $$\lim _{x \rightarrow-3}(|x|-2)$$

Evaluate the limits that exist. $$\lim _{x \rightarrow 0} \frac{x^{2}-2 x}{\sin 3 x}$$

Evaluate the limits that exist. $$\lim _{x \rightarrow 2} \frac{x-2}{x^{2}-4}$$

Decide in the manner of Section 2.1 whether or not the indicated limit exists. Evaluate the limits that do exist. $$\lim _{x \rightarrow 3} f(x) \text { if } f(x)=\left\\{\begin{aligned} x^{2}, & x<3 \\ 7, & x=3 \\ 2 x+3, & x>3 \end{aligned}\right.$$

Sketch the graph and classify the discontinuities (if any) as being removable or essential. If the latter, is it a jump discontinuity, an infinite discontinuity, or neither. $$h(x)=\left|x^{2}-1\right|$$.

Sketch the graph of a function \(f\) that is defined on [0,1] and meets the given conditions (if possible). \(f\) is continuous on [0,1] and non constant, takes on no integer values.

Decide on intuitive grounds whether or not the indicated limit exists; evaluate the limit if it does exist. $$\lim _{x \rightarrow 0} \frac{1}{|x|}$$