91Ó°ÊÓ

If you are given \(y=f(x),\) the equation of function \(f,\) describe how to find \(f^{\prime}(x)\).

Let \(f(x)=x^{3}-x^{2}+5 x-1\) and \(g(x)=2 .\) Find \(\lim _{x \rightarrow 3}(f \circ g)(x)\) and \(\lim _{x \rightarrow 3}(g \circ f)(x)\).

Let \(f(x)=x^{3}+x^{2}-6 x-1\) and \(g(x)=3 .\) Find \(\lim _{x \rightarrow 4}(f \circ g)(x)\) and \(\lim _{x \rightarrow 4}(g \circ f)(x)\).

graph each function. Then use your graph to find the indicated limit, or state that the limit does not exist. $$f(x)=\left\\{\begin{array}{ll} 3 x & \text { if } x<1 \\ x+2 & \text { if } x \geq 1, \lim _{x \rightarrow 1} f(x) \end{array}\right.$$

Explain how to use the derivative to compute the slopes of various tangent lines to the graph of a function.

Let \(f(x)=\frac{2}{x}\) and \(g(x)=\frac{3}{x-1} .\) Find \(\lim _{x \rightarrow 1}(f \circ g)(x)\) and \(\lim _{x \rightarrow 1}(g \circ f)(x)\).

Explain how the instantaneous rate of change of a function at a point is related to its average rates of change.

graph each function. Then use your graph to find the indicated limit, or state that the limit does not exist. $$f(x)=\left\\{\begin{array}{ll} x+1 & \text { if } x<0 \\ \sin x & \text { if } x \geq 0, \lim _{x \rightarrow 0} f(x) \end{array}\right.$$

graph each function. Then use your graph to find the indicated limit, or state that the limit does not exist. $$f(x)=\left\\{\begin{array}{ll} x & \text { if } x<0 \\ \cos x & \text { if } x \geq 0, \lim _{x \rightarrow 0} f(x) \end{array}\right.$$

Let \(f(x)=\frac{4}{x-1}\) and \(g(x)=\frac{1}{x+2} .\) Find \(\lim _{x \rightarrow 1}(f \circ g)(x)\) and \(\lim _{x \rightarrow 1}(g \circ f)(x)\).