MATH100 Study Guide - Final Guide: Maxima And Minima

dition.pdf In Exercises 11-16, use the Chain Rule to evaluate the partial derivative at the point specified 11, af/du and af/du at (u. u) = (-1,-1), where f(x, y, z) = x3 + 12. df/as at (r, s) = (1,0), where f(x,y)=ln(xy), x = 3r + 2s, y=5r + 3s ms g(x,y)=1/(x+y2), (r. θ)=(2V2,5), r sin θ where 13, ag/ae at x r cos θ, y x2-y2. x = 52 + 1, y = 1- 14. ag/as at s = 4, where gir, y) 2s 15, ag/au at (u, u) = (0, l ), where g(x, y) =エ2-y2, x = e" cos t, 16. dh at (q, r) = (3. 2), where h(u, u) “c". “ = q3.-gr2 dg 17. A baseball player hits the ball and then runs down the first base line at 20 fus. The first baseman fields the ball and then runs toward first base along the second base line at 18 fus as in Figure 7 Lectue P13 Sidepp

5.2 5.3 Chase Clay ton Worksheet 12 Math 165 Fall 2017 1. Let uer) and v(x) be functions of z and consider the function u(x) | f(t) dt u(x) F(x) = where f is a continuous function (a) Find an expression forf FG) (b) Compute this expression if u(x) sinx,r(x)-x2 cos(re), and f(x)-vz2sinz 2 Assuming that f(x) dx = 2 and g(z) dz -4, evaluate/2f (x) 3g(a) dr. -30-4) 3. Assunne that / 3/(r) dz--2, / 5f(x) dr 7, and f(z)--1 and evaluate f(x) da and 3f (x) +2 dz. 4. Since f(x) S If(a) for all z show that f(x) dx If(x)ld 5. Assume that for b > 0 that f(x) dx = 1-b-1. Use this to calculate the following: (a) f(x) dz. (b) 3f(x) -4da. 6. Use geometric reasoning to justify the following "facts" (a) If /(z) is even then Lf(z)dz=rf(z)dz. (b) If f(r) is odd then ()dr o.

5.2 5.3 Chase Clay ton Worksheet 12 Math 165 Fall 2017 1. Let uer) and v(x) be functions of z and consider the function u(x) | f(t) dt u(x) F(x) = where f is a continuous function (a) Find an expression forf FG) (b) Compute this expression if u(x) sinx,r(x)-x2 cos(re), and f(x)-vz2sinz 2 Assuming that f(x) dx = 2 and g(z) dz -4, evaluate/2f (x) 3g(a) dr. -30-4) 3. Assunne that / 3/(r) dz--2, / 5f(x) dr 7, and f(z)--1 and evaluate f(x) da and 3f (x) +2 dz. 4. Since f(x) S If(a) for all z show that f(x) dx If(x)ld 5. Assume that for b > 0 that f(x) dx = 1-b-1. Use this to calculate the following: (a) f(x) dz. (b) 3f(x) -4da. 6. Use geometric reasoning to justify the following "facts" (a) If /(z) is even then Lf(z)dz=rf(z)dz. (b) If f(r) is odd then ()dr o.