Tangent planes and linear approximation Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus-3/tangent-planes-and-linear-approximation/quiz/

1. 1

   Tangent plane to z = x² + y² at (1, 2). Find z.

   Answer: ____________________

2. 2

   Tangent plane to z = xy at (2, 3). Find z.

   Answer: ____________________

3. 3

   Tangent plane to z = 4 − x² − y² at (1, 1). Find z.

   Answer: ____________________

4. 4

   Tangent plane to z = 2x² + y² at (1, −1). Find z.

   Answer: ____________________

5. 5

   Tangent plane to z = x² − y² at (2, 1). Find z.

   Answer: ____________________

6. 6

   Tangent plane to f(x, y) = 2x² + xy at (1, −1)

   Answer: ____________________

7. 7

   Tangent plane to f(x, y) = xy² at (−1, 2)

   Answer: ____________________

8. 8

   Linear approximation of f(x, y) = xy² at (1, 2) to estimate f(1.1, 1.9)

   Answer: ____________________

9. 9

   Linear approximation of f(x, y) = xy at (2, 3) to estimate f(2.1, 2.9)

   Answer: ____________________

10. 10

    Linear approximation of f(x, y) = x³ − y² at (2, 1) to estimate f(1.9, 1.1)

    Answer: ____________________