Tangent planes and linear approximation Quiz
10 questions · easy to harder · Calculus 3 · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 0 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Tangent plane to z = x2 + y2 at (1, 2). Find z.Type the answer.
2 Question 2
Tangent plane to z = xy at (2, 3). Find z.Type the answer.
3 Question 3
Tangent plane to z = 4 − x2 − y2 at (1, 1). Find z.Type the answer.
4 Question 4
Tangent plane to z = 2x2 + y2 at (1, −1). Find z.Type the answer.
5 Question 5
Tangent plane to z = x2 − y2 at (2, 1). Find z.Type the answer.
6 Question 6
Tangent plane to f(x, y) = 2x2 + xy at (1, −1)Type the answer.
7 Question 7
Tangent plane to f(x, y) = xy2 at (−1, 2)Type the answer.
8 Question 8
Linear approximation of f(x, y) = xy2 at (1, 2) to estimate f(1.1, 1.9)Type the answer.
9 Question 9
Linear approximation of f(x, y) = xy at (2, 3) to estimate f(2.1, 2.9)Type the answer.
10 Question 10
Linear approximation of f(x, y) = x3 − y2 at (2, 1) to estimate f(1.9, 1.1)Type the answer.