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Magazine Problem 10
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number. $$h(x)=\frac{x+3}{\left(x^{2}-x-1\right)\left(x^{2}+1\right)} \quad \text { at } x=-2$$
Problem 11
Use the table feature of your calculator to find the limit. $$\lim _{x \rightarrow \pi^{-}} \frac{\sin x}{1-\cos x}$$
Problem 11
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number. $$f(x)=\frac{x \sqrt{x}}{(x-6)^{2}} \quad \text { at } x=36$$
Problem 11
Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow-2} \frac{3 x-1}{2 x+3}$$
Problem 12
Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 3} \frac{x^{2}+x+1}{x^{2}-2 x}$$
Problem 12
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number. $$k(x)=\frac{\sqrt{8-x^{2}}}{2 x^{2}-5} \quad \text { at } x=-2$$
Problem 12
Use the table feature of your calculator to find the limit. $$\lim _{x \rightarrow \frac{\pi}{2}^{-}}(\sec x-\tan x)$$
Problem 13
Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x^{2}-2 x-3}$$
Problem 13
Explain why the function is not continuous at the given number. $$f(x)=1 /(x-3)^{3} \quad \text { at } x=3$$
Problem 14
Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 1} \frac{x^{2}-1}{x^{2}+x-2}$$
