5. Evaluate the following differentials (a) det? (b) d sinh ở (c) dx sin (d) do...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...
10. Find the first derivative with respect to the independent variable for the following functions: (a) f(x) = sinh(4x) (b) g(t) = cosh(t) sinh(t). 1 - cosh(r) (c) h(r) = 1 + cosh(r) (d) F(X) = tanh(e). (e) y = sinh--(VT). (Hint: Apply implicit differentiation to sinh(y) = VT.) 11. Use appropriate hyperbolic function substitutions to evaluate the following indef- inite integrals: dc (a) /+) Ke-10) (e)/() dx (b) dar James G., Modern Engineering Mathematics (5th ed.) 2015.: Exercise set...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
dy For the following composite function, find an inner function u = g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dx y=tan (2x) Calculate the derivative of the following function. y = (5x - 19) dy Carry out the following steps for the given curve. dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point. x +y = 337;( - 4,3) a. Use implicit differentiation to find b....
1. In class, we examined in detail case "C" of table 3.4 on page 150 of your text. Prove the expressions provided in the table for cases A, B, and D. Specifically, start from the general equation 3.67, and apply at x-L the boundary condition on the second column of Table 3.4 for each of the cases. Then, solve the differential equation and acquire the information on the third and the fourth column. Hint In some cases, you will need...
for the following function (5 Marks) dy 5. (b) Use implicit differentiation to find dx 3x* - 6 ln(2xy) = 7-5e24-sy dy 1. (b) Evaluate: lim r? + 4x -12 (3-12x +1 (5 Marks)
ENG 1005 ASSIGNMENTI QUESTIONS (1) Use integration by parts to calculate sin(In(x) dx and Here, In is the natural logarithm. cos(In(x))dx. [5 marks (2) (a) Use integration by parts on sinh(t) sinh(t)dt and the identity cosh (1) = 1+sinh'in to calculate the integral of sinh(r). (b) Calculate the integral of sinh(r) by expanding the product and then integrating, Confirm that you get the same answer as in part (a). (e) Show that if x is a positive real number, then...
Find the exact value of the expressions cos(a +B), sin(Q+B) and tan(a +B) under the following conditions: sin(a) = 15 17 40 a lies in quadrant I, and sin(B) = 41 Blies in quadrant II. a. cos(a + b) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? dy dx (b) If x+y+z-9, dt 5, and -4, find dt dz dt when (x, y, z)-(2,2,1). Problem 2. (a) Find the derivative of the function yr e-****** (b) Find the derivative of the function y - In(x* +100). cos. Problem 3. Use logarithmic differentiation to find the derivative of the function...
find The Laplace Transform of ta sin (34) A.) (305²-54)/(32+9)3 B.) (185²-54)/(52+9)2 c.) (185²-54)/(s²+9)3 D) (305²-54) / (82 +9J² E.) (125²-54)/(3²+913 LC+2 e34) = find the Laplace transform Ali(5-3)3 2,25-32 B.)i|(5-3)?p.) 21(5-3)? Fidal (3-3) 1) X dy- yax=0 Linoer: X 4 y =o ou le =0 Seperebes Xdye ydx=d4= dy =oxy 24 =-, Not eg f(tx, ty) - ty - 1 Since equation is linar its not Renoulli * Classify the quation as homo exact Rorodhi X dy - y...