91Ó°ÊÓ

Use the method of replacement or end-behavior analysis to evaluate the limits. $$ \lim _{x \rightarrow 0^{+}} \frac{1}{\ln x} $$

In Activities 1 through \(26,\) write the formula for the derivative of the function. $$ f(x)=x^{5} $$

Write derivative formulas for the functions. $$ f(x)=\left(12.8 x^{2}+3.7 x+1.2\right)\left[29\left(1.7^{x}\right)\right] $$

In Activities 1 through \(30,\) for each of the composite functions, identify an inside function and an outside function and write the derivative with respect to \(x\) of the composite function. $$ f(x)=17 e^{0.7 x}+\pi $$

Give the derivative formula for each function. \(g(x)=6(0.8)^{x}\)

In Activities 1 through \(30,\) for each of the composite functions, identify an inside function and an outside function and write the derivative with respect to \(x\) of the composite function. $$ f(x)=2 e^{0.5 x}-2 x $$

Gross Domestic Product The GDP of a certain country is \(\$ 615\) billion and is increasing by \(\$ 25\) thousand per person. The population of that country is 74 million and is increasing by 0.7 million people per year. How quickly is the GDP increasing?

Use the method of replacement or end-behavior analysis to evaluate the limits. $$ \lim _{x \rightarrow 2} \frac{1}{x-2} $$

In Activities 1 through \(26,\) write the formula for the derivative of the function. $$ f(x)=x^{4} $$

Write derivative formulas for the functions. $$ f(x)=(5 x+29)^{5}(15 x+8) $$