question 1

Find the partial derivative of the dependent variable with respect to each of the independent variables. Z= (3x2 + x/3)7 dz = 7(3x2 + xy3, 6(6* + 3) dzThe volume V of a right circular cylinder is given by V = it - h, where r is the radius and h is the height. If h is held fixed at h = 6 inches, find the rate of change of V with respect to r when r = 10 inches. The rate is in2. (Type an exact answer in terms of It.)The current i in a certain electric circuit is i = 12 sin at. Write the first three terms of the Taylor series of this function about t = 2 Choose the correct answer below. 372 372 2 O A. 12 sin + 121 COS t - 2 - 121- sin t - 2 2 2 2 2 O B. 12 sin + 12 cos t - 2 - 12 sin t - 2 2 2 2 372 2 O C. 12 sin + 12 cos t - - 6 sin t - 2 2 2 2 2 372 2 D. 12 sin + 121 cos - 61 sin + ". 2 2 t - 2 2 t - 2Solve the given differential equation. dy = x48 - y dx Choose the correct answer below. 4 X O A. V= 8- + C 4 OB. 814 -y =e X + C 2 O C. 48-y = 4e X + C 2 OD. 418-y =e X + CSolve the given differential equation. I'ydx "may + age): = Ed): The solution is E. {Type an equation.) Find the particular solution to the given differential equation that satisfies the given conditions. + y- dy = 9(xdx + ydy); x =0 when y =27 The particular solution is (Type an equation.)Solve the given differential equation. The form of yo is given. Day + 2Dy - 15y = 45 (Let yp = A.) Choose the correct solution below. c, and c, are arbitrary constants. O A. y=ce +cze -5% + 45 O B. y=Ce + Cye- 5x O C. y=ce +cge" "- 3 O D. y=Cqex + Cze - 5X - 303xFind the general solution of the given equation. v" - 4y' + 3y = 0 Choose the correct solution below. c, and c, are arbitrary constants. OA. y=Gye* + coxe* O B. y=Gqe + Cze* O c. y= , cos (X) + C2 sin (3x) OD. y=GetexFind the general solution of the given equation. v" - 4y' + 3y = 0 Choose the correct solution below. c, and c, are arbitrary constants. OA. y=Gye* + coxe* O B. y=Gqe + Cze* O c. y= , cos (X) + C2 sin (3x) OD. y=GetexFor a given circuit, L =6 mH, R =0, C= 40 nF, and E = 0. Find the equation relating the charge and the time if q = 10" C and i = 0 when t = 0. . . . Choose the correct equation below. O A. q = 100,000 cos 0.0645t O B. q = 100,000 cos 64,550t O c. q= cos 64,550t O D. q = 100,000 sin 64,550tFind at least three nonzero terms (including a, and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given function, and 6 -TEX