On the moon the acceleration due to gravity is 5 ft/sec. An astronaut jumps into the air with an initial upward velocity of 11 ft/sec. How high does she/he go? feet How long is the astronaut off the ground? sec. Note: You can earn partial credit on this problem. (a) 130/90- Calculate the following antiderivatives: 41 5 cll = | | -0. dt 1 (b) u1/4 +6.5udu = C 1 (c) 26 d = +C. Note: You can earn partial credit on this problem. 5 Find the linear approximation L(x) of f(x) = ln (6-4x) at x = and use it to estimate In (0.91). 4 L(x) = and In (0.91) Note: You can earn partial credit on this problem. Find the most general version of the following integral. Note that you can check your answer by differentiation. (t+5) 14 dt (1 point) The Volume of a cone is given by V = (1/3)(*) HR2 where H is the height of the cone and R is the radius of the circular base. The radius is increased by 3%. Using differentials, the approximate change (in percent change) of the Volume of the cone is The volume of a cone is given by V = rh, where he is the height of the cone and r is the radius of the circular base. A cone has a height of 6cm. If the radius is increased from 5cm. to 5.3 cm. a) Find the exact change (AV) in the volume of the cone. AV = b) Find the approximate change (dV) in the volume using differentials. dv=0 Note: to be sure that your answers are graded correctly, either enter a mathematical expression for each quantity, or enter each answer to at least 8 decimal places. Note: You can earn partial credit on this problem. Find the local linear approximation of the function f(x)=5+zat z=11, and use it to approximate 15.9 and 16.1. (a) f(x)=5+2= (b) 15.9 15.9 (c) 16.1 0 For parts (b) and (c), you should enter your answer as a fraction. If you enter a decimal, make sure that it is correct to at least six decimal places. Note: You can earn partial credit on this problem. Suppose that f3e5* dx = (Ar + B)e** + C for some constants A, B and C. Find the values of A and B: and B A=0 ar Hint: If f(x)dx = F(x) + C then F'(x) = f(x). Note: You can earn partial credit on this problem. Find the particular antiderivative that satisfies the following conditions: f"(x)=20x-10; f(0) = 4, f'(0) = -4 f(x) = Suppose and F is an antiderivative of f that satisfies f(x) = x+ sinc Then F(x) F(x)=0.