v. \( f(x)=\frac{\arcsin 3 x}{x} \)

9/16/24, 1:31 \( P M \) 16. Find \( f^{\prime}(x) \) using the rules for finding derivatives, \( f(x)=\frac{6 x-2}{x-2} \) \( f^{\prime}(x)=\square \)

a. Use the definition \( m_{\tan }=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h} \) to find the slope of the line tangent to the graph of \( f \) at \( P \). Online Assignment 2-Abdulaziz Jahdali (b. Determine an equation of the tangent line at \( P \). 10. \( f(x)=x^{2}+1, P(-2,5) \) a. \( m_{\tan }=\square \) b. \( y=\square \)

15. Find \( f^{\prime}(x), f^{\prime \prime}(x) \), and \( f^{(3)}(x) \) for the following function. \[ f(x)=8 x^{3}+4 x^{2}+9 x \] \( f^{\prime}(x)=\square \) \( f^{\prime \prime}(x)=\square \) \( f^{(3)}(x)=\square \) https://tdx.acs.pearson.com/api//41/print/highered

3. Evaluate the following limit. \( \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1} \) Rewrite the given limit in a way that can be evaluated by direct substitution. \( \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1}=\lim _{x \rightarrow-1} \) (Simplify your answer.) \( \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1}=\square \) (Type an exact answer.)

Find the limit of the polynomial \( p(x) \) as \( x \) approaches \( -\infty \) \[ p(x)=4 x^{7}-7 x^{6}+1 \] The limit of \( p(x) \) as \( x \) approaches \( -\infty \) is