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Magazine Problem 250
For the following exercises, use numerical evidence to determine whether the limit exists at \(x=a\). If not, describe the behavior of the graph of the function at \(x=a\). $$f(x)=\frac{-2}{x-4} ; a=4$$
Problem 251
For the following exercises, use numerical evidence to determine whether the limit exists at \(x=a\). If not, describe the behavior of the graph of the function at \(x=a\). $$f(x)=\frac{-2}{(x-4)^{2}} ; a=4$$
Problem 252
For the following exercises, use numerical evidence to determine whether the limit exists at \(x=a\). If not, describe the behavior of the graph of the function at \(x=a\). $$f(x)=\frac{-x}{x^{2}-x-6} ; a=3$$
Problem 253
For the following exercises, use numerical evidence to determine whether the limit exists at \(x=a\). If not, describe the behavior of the graph of the function at \(x=a\). $$f(x)=\frac{6 x^{2}+23 x+20}{4 x^{2}-25} ; a=-\frac{5}{2}$$
Problem 254
For the following exercises, use numerical evidence to determine whether the limit exists at \(x=a\). If not, describe the behavior of the graph of the function at \(x=a\). $$f(x)=\frac{\sqrt{x}-3}{9-x} ; a=9$$
Problem 255
For the following exercises, determine where the given function \(f(x)\) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. $$f(x)=x^{2}-2 x-15$$
Problem 256
For the following exercises, determine where the given function \(f(x)\) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. $$f(x)=\frac{x^{2}-2 x-15}{x-5}$$
Problem 257
For the following exercises, determine where the given function \(f(x)\) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. $$f(x)=\frac{x^{2}-2 x}{x^{2}-4 x+4}$$
Problem 258
For the following exercises, determine where the given function \(f(x)\) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. $$f(x)=\frac{x^{3}-125}{2 x^{2}-12 x+10}$$
Problem 259
For the following exercises, determine where the given function \(f(x)\) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. $$f(x)=\frac{x^{2}-\frac{1}{x}}{2-x}$$
