
Linearization

Click on each problem to expand and view the problem. You can then download a solution to the problem in PDF format. You can collapse the problem by clicking on the problem again.

• Exam 2, Fall 2009, Problem 4

• Exam 2, Fall 2009, Problem 3

• Exam 2, Practice Fall 2009, Problem 19

• Exam 2, Spring 2011, Problem 5

• Exam 2, Fall 2012, Problem 5

Let $f$ be a function such that $f(3)=1$ and $f'(3)=2$.

(a) Use the linear approximation of $f$ about $x=3$ to estimate $f(3.1)$.

(b) Let $g$ be the inverse of $f$. Find $g(1)$ and $g'(1)$.

• Exam 2, Spring 2013, Problem 3

Use linearization to estimate the following quantities:

(a) $\ln(0.98)$

(b) $\sin(0.02)$

In each case indicate whether your answer is an underestimate or an overestimate.

• Exam 2, Study Guide, Problem 5

• Exam 2, Study Guide, Problem 6

• Final Exam, Fall 2010, Problem 8

• Final Exam, Fall 2011, Problem 7

• Final Exam, Spring 2012, Problem 4

Use a linear approximation to estimate each quantity. Clearly indicate the function and the point where you are taking the linear approximation.

(a) $\sqrt{79}$

(b) $\ln(1.067)$

• Final Exam, Study Guide, Problem 15