91Ó°ÊÓ

Classify each statement as either true or false. $$\lim _{x \rightarrow 3} 7=7$$

Differentiate each function. $$y=(7-x)^{55}$$

Classify each statement as either true or false. If \(\lim _{x \rightarrow 4} F(x)=7,\) then \(\lim _{x \rightarrow 4}[c \cdot F(x)]=7 c.\)

Classify each statement as either true or false. If \(f\) is continuous at \(x=2,\) then \(f(2)\) must exist.

Use the Theorem on Limits of Rational Functions to find the following limits. When necessary, state that the limit does not exist. $$\lim _{x \rightarrow-2}\left(x^{2}+3\right)$$

In Exercise : a) Graph the function. b) Draw tangent lines to the graph at points whose \(x\) -coordinates are \(-2,0,\) and 1. c) Find \(f^{\prime}(x)\) by determining \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}.\) d) Find \(f^{\prime}(-2), f^{\prime}(0),\) and \(f^{\prime}(1) .\) These slopes should match those of the lines you drew in part ( \(b\) ). $$f(x)=x^{2}-x$$

Differentiate two ways: first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your results as a check. $$G(x)=\frac{8 x^{3}-1}{2 x-1}$$

Differentiate two ways: first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your results as a check. $$y=\frac{t^{2}-25}{t-5}$$

The initial substitution of \(x=a\) yields the form \(0 / 0 .\) Look for ways to simplify the function algebraically, or use a table and/or a graph to determine the limit. When necessary, state that the limit does not exist. $$\lim _{x \rightarrow 1} \frac{x^{2}+5 x-6}{x^{2}-1}$$

Differentiate each function. $$f(x)=x^{2} \sqrt{4 x-1}$$