91Ó°ÊÓ

Evaluate the following limits. \(\lim _{x \rightarrow 4}(3 x-7)\)

Let \(f(x)=\frac{x^{2}-4}{x-2}\) a. Calculate \(f(x)\) for each value of \(x\) in the following table. b. Make a conjecture about the value of \(\lim _{x \rightarrow 2} \frac{x^{2}-4}{x-2}\)

The table gives the position \(s(t)\) of an object moving along a line at time \(t,\) over a two-second interval. Find the average velocity of the object over the following intervals. a. [0,2] b. [0,1.5] c. [0,1] d. [0,0.5]

Evaluate the following limits. \(\lim _{x \rightarrow 1}(-2 x+5)\)

Let \(f(x)=\frac{x^{3}-1}{x-1}\) a. Calculate \(f(x)\) for each value of \(x\) in the following table. b. Make a conjecture about the value of \(\lim _{x \rightarrow 1} \frac{x^{3}-1}{x-1}\)

Evaluate the following limits. $$\lim _{x \rightarrow \infty} \frac{3+2 x+4 x^{2}}{x^{2}}$$

Evaluate the following limits. \(\lim _{x \rightarrow-9} 5 x\)

Continuity at a point Determine whether the following functions are continuous at a. Use the continuity checklist to justify your answer. $$f(x)=\frac{2 x^{2}+3 x+1}{x^{2}+5 x} ; a=5$$

Evaluate the following limits. $$\lim _{x \rightarrow \infty} \frac{\cos x^{5}}{\sqrt{x}}$$

Let \(f(x)=x^{3}+3\) and note that \(\lim _{x \rightarrow 0} f(x)=3\) For each value of \(\varepsilon,\) use a graphing utility to find all values of \(\delta>0\) such that \(|f(x)-3|<\varepsilon\) whenever \(0<|x-0|<\delta .\) Sketch graphs illustrating your work. a. \(\varepsilon=1\) b. \(\varepsilon=0.5\)