Brilliant

Today Courses

Practice

Algebra
Geometry
Number Theory
Calculus
Probability
Basic Mathematics
Logic
Classical Mechanics
Electricity and Magnetism
Computer Science
Quantitative Finance
Chemistry

rocket with vector

Excel in math and science.

Log in with Facebook Log in with Google Log in with email

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

rocket with vector

Your answer seems reasonable. Find out if you're right!

Sign up to access problem solutions.

That seems reasonable. Find out if you're right!

Sign up to save your progress!

Log in with Facebook Log in with Google Log in with email

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Taylor Series

Concept Quizzes

Local Linear Approximation
Taylor Series
Taylor Series Approximation
Taylor Series Manipulation
Taylor Series - Interval and Radius of Convergence
Taylor Series - Error Bounds
Taylor Series - Problem Solving

Challenge Quizzes

Taylor Series: Level 3 Challenges
Taylor Series: Level 4 Challenges
Taylor Series: Level 5 Challenges

Local Linear Approximation

If $f(1)=4$ and $f'(1)=6,$ which of the following is the best local linear approximation for $f(1.01)?$

4.60 4.30 7.00 4.06

Show explanation

by Brilliant Staff

Estimate the value of $\sqrt[3]{0.979}$ using local linear approximation for the function $f(x)=\sqrt[3]{1+x}.$

0.972 0.986 0.993 0.965

Show explanation

by Brilliant Staff

Use differentiation to estimate the value of $\sqrt{16.5}$ .

4.062 4.124 4.186 4.248

Show explanation

by Brilliant Staff

Estimate the value of $\displaystyle \frac{6}{(1-x)^2}$ at $x=0.02$ using local linear approximation.

6.12 6.24 6.60 6.48

Show explanation

by Brilliant Staff

What is the local linear approximation of the function $f(x)=14x^3-5x$ near $x = 1?$

{42}x^2+5

{42}x^2-5

{37}x-28

{37}x+28

Show explanation

by Brilliant Staff

×

Problem Loading...

Note Loading...

Set Loading...