University:
Whitman College
Course:
MATH-225 | Calculus III
Academic year:

2024
Views:

86

Pages:

1
Author:

Quinn Watkins

Supplementary Exercises for Sections 13.3 1. Explain in your own words why, when taking a partial derivative of a function of multiple variables, we can treat the variables not being differentiated as constants. 2. Consider a differentiable function, f (x, y). Give physical interpretations of the meanings of fx (a, b) and fy (a, b) as they relate to the graph of f . 3. In much the same way that we used the tangent line to approximate the value of a function from single variable calculus, we can use the tangent plane to approximate a function from multivariable calculus. Consider the tangent plane found in Exercise 11. Use this plane to approximate f (1.98, .4). 4. Suppose that one of your colleagues has calculated the partial derivatives of a given function, and reported to you that fx (x, y) = 2x + 3y and that fy (x, y) = 4x + 6y. Do you believe them? Why or why not? If not, what answer might you have accepted for fy ? 5. Suppose f and g are single variable differentiable functions. Find the (a) z = f (x)g(y) (b) z = f (xy) (c) z = f (x/y) 1 ∂z ∂x and ∂z ∂y in each case

Supplementary Exercises for Sections 13.3

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