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Find a degree 
Magazine Problem 54
Find the equation of the tangent line to the function \(f\) at the given point. Then graph the function and the tangent line together. $$f(x)=\sqrt{x} \text { at }(4,2)$$
Problem 55
Evaluate each limit. (a) \(\lim _{x \rightarrow 10} \log x\) (b) \(\lim _{x \rightarrow-1} \log x\) (c) \(\lim _{x \rightarrow 0} \log x\)
Problem 55
Evaluate each limit. $$\begin{array}{l} \text { (a) } \lim _{x \rightarrow 2^{-}} \ln (x-2) \\ \text { (b) } \lim _{x \rightarrow 2^{+}} \ln (x-2) \\ \text { (c) } \lim _{x \rightarrow 2} \ln (x-2) \end{array}$$
Problem 55
Find \(f^{\prime}(x)\) using the alternative definition. $$f(x)=-x^{2}+4 x$$
Problem 55
Use a table and/or graph to decide whether each limit exists. If a limit exists, find its value. \(\lim _{x \rightarrow 1} \frac{\ln x^{2}}{\ln x}\)
Problem 56
Use a table and/or graph to decide whether each limit exists. If a limit exists, find its value. \(\lim _{x \rightarrow 0} \frac{e^{-x}-1}{x}\)
Problem 56
Evaluate each limit. (a) \(\lim _{x \rightarrow e^{3}} \ln |x|\) (b) \(\lim _{x \rightarrow-1} \ln |x|\) (c) \(\lim _{x \rightarrow 0} \ln |x|\)
Problem 56
Evaluate each limit. $$\begin{array}{l} \text { (a) } \lim _{x \rightarrow \pi^{-}} \cot x \\ \text { (b) } \lim _{x \rightarrow \pi^{+}} \cot x \\ \text { (c) } \lim _{x \rightarrow \pi} \cot x \end{array}$$
Problem 57
Evaluate each limit. (a) \(\lim _{x \rightarrow 0} \tan x\) (b) \(\lim _{x \rightarrow \infty / 2} \tan x\) (c) \(\lim _{x \rightarrow 3 \pi / 4} \tan x\)
Problem 57
Find \(f^{\prime}(x)\) using the alternative definition. $$f(x)=2 x^{2}-x$$
