Math32aHW7
All numbered problems are from the textbook Multivariable
Calculus by Rogawski (2nd edition).
1. If f(x, y) = x(x2 + y2)3/2esin x2y, find fx(1, 0) (Hint:
instead of computing fx(x, y) and then plugging in (1, 0),
compute fx(1, 0) by using directly the definition of partial
derivative at the point (1, 0));
2. Problem 15.3.84;
3. Problem 15.4.6;
4. Problem 15.4.12;
5. Problem 15.4.18;
6. Problem 15.4.30;
7. Problem 15.4.32 (I = W/H2);
8. Problem 15.4.39. Hint: youre given that |r| 0.05 3.52 and |h|
0.05 6.2 (or, equivalently, |dr| 0.05 3.52
and |dh| 0.05 6.2, since r = dr, h = dh (warning: V 6= dV
!));
9. Problem 15.4.41 (locally linear = differentiable);
10. Problem 15.4.43;
11. Four positive numbers, each between 0 and 10, are rounded
down to an integer, and then multiplied together.Use differentials
to estimate the maximum possible error in the computed product that
might result from thisrounding.
12. Consider the function z = f(x, y) = x2 xy + 3y2 around the
point (3,1). Compute:
(i) Linearization function L(x, y) of f at the point (3,1);(ii)
Differential dz at (3,1);
Now suppose that (x, y) changes from (3,1) to (2.96,0.95).
Compute
(iii) z during this change;
(iv) dz during this change;
(v) f(2.96,0.95);(vi) L(2.96,0.95);(vii) What is the error if
you were to approximate z by dz? What is the error if you were to
approximate
f(2.96,0.95) by L(2.96,0.95)?
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