Suggested languages for you:

Americas

Europe

Problem 10

Complete the table by computing \(f(x)\) at the given values of \(x\). Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=2 x^{2}-1 ; \lim _{x \rightarrow 1} f(x) \\ \hline x \quad 0.9 \quad 0.99 \quad 0.999 \quad 1.001 \quad 1.01 \quad 1.1 \\ \hline f(\boldsymbol{x}) & & & & & & \\ \hline \end{array} $$

Expert verified

Based on the table and the behavior of the function values as \(x\) approaches 1, we can estimate that the limit \(\lim _{x \rightarrow 1} (2x^2 - 1)\) does exist and is approximately equal to 1.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 9

Find the derivative of each function. \(f(x)=(2 x+1)^{-2}\)

Chapter 9

AIR PURIFICATION During testing of a certain brand of air purifier, the amount of smoke remaining \(t\) min after the start of the test was $$ \begin{aligned} A(t)=&-0.00006 t^{5}+0.00468 t^{4}-0.1316 t^{3} \\ &+1.915 t^{2}-17.63 t+100 \end{aligned} $$ percent of the original amount. Compute \(A^{\prime}(10)\) and $A^{\prime \prime}(10)$ and interpret your results. Source: Consumer Reports

Chapter 9

Find the derivative of each function. \(f(x)=\sqrt[3]{1-x^{2}}\)

Chapter 9

Find the derivative of each function. \(f(x)=\frac{1}{(2 x+3)^{3}}\)

Chapter 9

Find the derivative of each function. \(f(x)=\sqrt{2 x^{2}-2 x+3}\)

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner