Chapter 2: Problem 30
Horizontal Tangent At what point is the tangent to \(f(x)=3-4 x-x^{2}\) horizontal?
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
In Exercises \(67 - 70\) , use the following function. \(f ( x ) = \left\\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.\) Multiple Choice What is the value of \(\lim _ { x \rightarrow 1 } f ( x ) ?\) \(( \mathrm { A } ) 5 / 2 \quad ( \mathrm { B } ) 3 / 2\) (C) 1 (D) 0 (E) does not exist
In Exercises \(67 - 70\) , use the following function. \(f ( x ) = \left\\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.\) Multiple Choice What is the value of \(\lim _ { x \rightarrow 1 } + f ( x ) ?\) (A) 5\(/ 2\) \(( \mathrm { B } ) 3 / 2\) \(( \mathbf { C } ) 1\) \(( \mathbf { D } ) 0\) (E) does not exist
In Exercises \(55 - 58 ,\) complete parts \(( a ) - ( d )\) for the piecewise- definedfunction. \(\quad (\) a) Draw the graph of \(f\) . (b) At what points \(c\) in the domain of \(f\) does \(\lim _ { x \rightarrow c } f ( x )\) exist? (c) At what points \(c\) does only the left-hand limit exist? (d) At what points \(c\) does only the right-hand limit exist? $$f ( x ) = \left\\{ \begin{array} { l l } { \sqrt { 1 - x ^ { 2 } } , } & { 0 \leq x < 1 } \\ { 1 , } & { 1 \leq x < 2 } \\ { 2 , } & { x = 2 } \end{array} \right.$$
In Exercises \(7 - 14 ,\) determine the limit by substitution. Support graphically. $$\lim _ { x \rightarrow - 1 / 2 } 3 x ^ { 2 } ( 2 x - 1 )$$
In Exercises \(67 - 70\) , use the following function. \(f ( x ) = \left\\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.\) Multiple Choice What is the value of \(f ( 1 ) ?\) (A) 5\(/ 2 \quad\) (B) 3\(/ 2 \quad\) (C) (D) 0 1(E) does not exist
What do you think about this solution?
We value your feedback to improve our textbook solutions.
