11 Calculus Questions

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I need the first 11 questions of the assignment done.

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WebAssign 15.2 (Homework) Current Score : 1 / 107 Khaled Omar MAT 211, section TTH Sp19 15409, Spring 2019 Instructor: Jay Abramson Due : Tuesday, January 29, 2019 11:59 PM MSTLast Saved : n/a Saving... () 1. –/4 pointsWaneFMAC7 15.2.002. Calculate ∂f , ∂f , ∂f ∂x ∂y ∂x UNDEFINED.) , and (1, −1) f(x, y) = 1,500 + 5x − 2y ∂f = ∂x ∂f = ∂y ∂f ∂x ∂f ∂y (1, −1) (1, −1) = = ∂f ∂y when defined. (If an answer is undefined, enter (1, −1) 2. –/4 pointsWaneFMAC7 15.2.003. Calculate ∂f , ∂f , ∂f ∂x ∂y ∂x UNDEFINED.) , and (1, −1) f(x, y) = 5x2 − y3 + x − 2 ∂f = ∂x ∂f = ∂y ∂f ∂x ∂f ∂y (1, −1) (1, −1) = = ∂f ∂y when defined. (If an answer is undefined, enter (1, −1) 3. –/4 pointsWaneFMAC7 15.2.007. Calculate ∂f , ∂f , ∂f ∂x ∂y ∂x UNDEFINED.) f(x, y) = 6x2y ∂f = ∂x ∂f = ∂y ∂f ∂x ∂f ∂y (1, −1) (1, −1) = = , and (1, −1) ∂f ∂y when defined. (If an answer is undefined, enter (1, −1) 4. –/4 pointsWaneFMAC7 15.2.010. Calculate ∂f , ∂f , ∂f ∂x ∂y ∂x UNDEFINED.) , and (1, −1) f(x, y) = x−5y2 + xy2 + 5xy ∂f = ∂x ∂f = ∂y ∂f ∂x ∂f ∂y (1, −1) (1, −1) = = ∂f ∂y when defined. (If an answer is undefined, enter (1, −1) 5. –/4 pointsWaneFMAC7 15.2.012. Calculate ∂f , ∂f , ∂f ∂x ∂y ∂x , and (1, −1) UNDEFINED.) f(x, y) = ∂f = ∂x ∂f = ∂y ∂f ∂x ∂f ∂y = (1, −1) = (1, −1) 2 (xy + 1)1 ∂f ∂y when defined. (If an answer is undefined, enter (1, −1) 6. –/4 pointsWaneFMAC7 15.2.018. Calculate ∂f , ∂f , ∂f ∂x ∂y ∂x , and (1, −1) UNDEFINED.) f(x, y) = 8xe5xy ∂f = ∂x ∂f = ∂y ∂f ∂x ∂f ∂y = (1, −1) = (1, −1) ∂f ∂y when defined. (If an answer is undefined, enter (1, −1) 7. –/8 pointsWaneFMAC7 15.2.020. Find ∂2f , ∂2f , ∂2f , and ∂2f . ∂y∂x ∂x2 ∂y2 ∂x∂y f(x, y) = 1,000 + 4x − 6y ∂2f = ∂x2 ∂2f = ∂y2 ∂2f = ∂x∂y ∂2f = ∂y∂x Evaluate them all at (1, −1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂2f (1, −1) = ∂x2 ∂2f (1, −1) = ∂y2 ∂2f (1, −1) = ∂x∂y ∂2f (1, −1) = ∂y∂x 8. –/8 pointsWaneFMAC7 15.2.023. Find ∂2f , ∂2f , ∂2f , and ∂2f . ∂y∂x ∂x2 ∂y2 ∂x∂y f(x, y) = 2x2y ∂2f = ∂x2 ∂2f = ∂y2 ∂2f = ∂x∂y ∂2f = ∂y∂x Evaluate them all at (1, −1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂2f (1, −1) = ∂x2 ∂2f (1, −1) = ∂y2 ∂2f (1, −1) = ∂x∂y ∂2f (1, −1) = ∂y∂x 9. –/8 pointsWaneFMAC7 15.2.026. Find ∂2f , ∂2f , ∂2f , and ∂2f . ∂y∂x ∂x2 ∂y2 ∂x∂y f(x, y) = e2x + y ∂2f = ∂x2 ∂2f = ∂y2 ∂2f = ∂x∂y ∂2f = ∂y∂x Evaluate them all at (1, −1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂2f (1, −1) = ∂x2 ∂2f (1, −1) = ∂y2 ∂2f (1, −1) = ∂x∂y ∂2f (1, −1) = ∂y∂x 10.–/6 pointsWaneFMAC7 15.2.032. Find ∂f , ∂f , and ∂f . HINT [See Example 3.] ∂x ∂y ∂z f(x, y, z) = 32 x2 + y2 + z2 ∂f = ∂x ∂f = ∂y ∂f = ∂z Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂f (0, −1, 1) = ∂x ∂f (0, −1, 1) = ∂y ∂f (0, −1, 1) = ∂z 11.–/6 pointsWaneFMAC7 15.2.034. Find ∂f , ∂f , and ∂f . HINT [See Example 3.] ∂x ∂y ∂z f(x, y, z) = 8xyez + 9xeyz + exyz ∂f = ∂x ∂f = ∂y ∂f = ∂z Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂f (0, −1, 1) = ∂x ∂f (0, −1, 1) = ∂y ∂f (0, −1, 1) = ∂z 12.–/6 pointsWaneFMAC7 15.2.036. Find ∂f , ∂f , and ∂f . HINT [See Example 3.] ∂x ∂y ∂z f(x, y, z) = 6x0.1y0.9 + z2 ∂f = ∂x ∂f = ∂y ∂f = ∂z Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂f (0, −1, 1) = ∂x ∂f (0, −1, 1) = ∂y ∂f (0, −1, 1) = ∂z 13.–/6 pointsWaneFMAC7 15.2.037. Find ∂f , ∂f , and ∂f . HINT [See Example 3.] ∂x ∂y ∂z f(x, y, z) = 21exyz ∂f = ∂x ∂f = ∂y ∂f = ∂z Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂f (0, −1, 1) = ∂x ∂f (0, −1, 1) = ∂y ∂f (0, −1, 1) = ∂z 14.–/6 pointsWaneFMAC7 15.2.039. Find ∂f , ∂f , and ∂f . HINT [See Example 3.] ∂x ∂y ∂z f(x, y, z) = 4,000z 1 + y0.8 ∂f = ∂x ∂f = ∂y ∂f = ∂z Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂f (0, −1, 1) = ∂x ∂f (0, −1, 1) = ∂y ∂f (0, −1, 1) = ∂z 15.–/6 pointsWaneFMAC7 15.2.040. Find ∂f , ∂f , and ∂f . HINT [See Example 3.] ∂x ∂y ∂z f(x, y, z) = e0.5x 1 + e−0.2y ∂f = ∂x ∂f = ∂y ∂f = ∂z Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) ∂f (0, −1, 1) = ∂x ∂f (0, −1, 1) = ∂y ∂f (0, −1, 1) = ∂z 16.–/9 pointsWaneFMAC7 15.2.060. A production formula for a student's performance on a difficult English examination is given by g(t, x) = 4tx − 0.2t2 − x2, where g is the grade the student can expect to get, t is the number of hours of study for the examination, and x is the student's grade-point average. (a) Calculate gt(10, 3) and gx(10, 3). gt(10, 3) = gx(10, 3) = Interpret the results. If you have studied for hours and have a GPA of the examination is increasing by and by (b) What does the ratio , your score on points for each additional hour of study points for each additional point of GPA. gt(10, 3) tell about the relative merits of study and grade-point gx(10, 3) average? At a level of hours of study with a GPA of of study is equivalent to an increase of GPA (as far as your test score is concerned). , one additional hour (rounded to three decimal places) in 17.1/14 points | Previous AnswersWaneFMAC7 15.2.064. Recall that the compound interest formula for continuous compounding is A(P, r, t) = Pert where A is the future value of an investment of P dollars after t years at an interest rate of r. (a) Calculate ∂A , ∂A , and ∂A , all evaluated at (90, 0.1, 10). (Round your answers to two ∂P ∂r ∂t decimal places.). ∂A = ∂P ∂A = ∂r ∂A = ∂t Interpret your answers. For a $ investment at % interest invested for years and compounded continuously, the accumulated amount is increasing at a rate of $ per $1 of principal, at a rate of $ rate of $ per increase of 1 in r, and at a per year. (b) What does the function ∂A ∂P of t tell about your investment? (90, 0.1, t) AP(90, 0.1, t) tells you the rate at which the accumulated amount in an account bearing % interest, compounded continuously, with a principal of $ growing per $1 ---Select--- after the investment. in the principal , , is years
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