3A (2) on point {graded} gW Find the linear approximation for h/R % 0 for w = W the weight of a satellite at altitude 11. above the earth's 1 + B surface, where W is the mass of the satellite on earth's surface and R is the radius of the earth. w(h) % 3A (3) 1 point possible (graded) (This problem is completely unrelated to the previous problem.) In this problem, assume that mass is proportional to volume, and that volume is proportional to the height cubed of a person. If a person 5 feet tall weighs on the average 120 lbs.I approximately how much does a person 5'1\" tall weigh? 3A (4) \"I point possible [graded] Find a quadratic approximation to tan (9), for I9 m 0. (Type theta for 9.) 1'09)m 3A (5) 1 point possible (graded) Find the quadratic approximation to sec c for x ~0. V1 - x2 f (ac) ~3A (6) 1 point possible (graded) Find the quadratic approximation to 1/ (1 - x) , for a ~ 1/2. (Use the basic approximations.) f (20) ~3A (7) 1 point possible [graded] For an ideal gas at constant temperature, the variables p (pressure) and '0 (volume) are related by the equation 3311'\" = c, where k and c are constants. If the volume is changed slightly from v to v + Av, what quadratic approximation expressing p in terms of 1), A1), 6 and I: would you use? (Find the approximation valid for At? a: 0. Enter Dv for At). Type a: for multiplicaton; ,l for division; /\\ for exponentiation.) p(v+Av)W 3A (8) 0/1 point (graded) Find the quadratic approximation of near * = 0. 1 - x f (a)3A (*) (9) 1 point possible (graded) In (1 + x) Find the linear approximation of near * = 0. f (2) ~3A (10) 1 point possible (graded) Find the quadratic approximation of In cos a near x = 0. f (a) ~3A (11) 1 point possible [graded] Find the quadratic approximation of 2:111 a: near a: = 1. (Hint: put a: = 1 + h.) f0\") W 3A (12} 2 points possible {graded} Find the linear and quadratic approximation to the following functions. sin (23:), near a: = 0 linear: f {at} m quadratic: f(m) m 3A (13) 2 points possible (graded) COS (2x), near x = 0 linear: f (a) ~ quadratic: f (a) ~3A (14) 2 points possible (graded) sec (a ), near * = 0 linear: f (a) ~ quadratic: f (2) ~3A (15) 1 point possible [graded] Find a positive initial guess can for the positive zero of a: $3 = 0 for which Newton's method gives an undefined quantity for 2:1. (Type :1: for multiplication; type f for division; type /\\ for exponentiation. You may type sqrt for / . You may also enter answer as a decimal correct to 3 decimal places.) 23}: 3A {16) 1 point possible [graded] Find a positive initial guess $3 for the zero of m 9:3 = 0 for which Newton's method bounces back and forth infinitely. (Use symmetry.) (Type a: for multiplication; type ,-' for division; type A for exponentiation. You may type sqrt for f. You may also enter answer as a decimal correct to 3 decimal places.) 93'}: 3A (17) 3 points possible (graded) Find the largest interval around each of the roots 3 $3 = 0 such that Newton's method converges to that root for every initial guess $3 in that interval. (Use your previous two answers here.) (Enter answer as an interval (a, b). Enter infty for 00 and -lnfty for 00. Use round parentheses. You may type sqrt(2) for x/E etc. Type * for multiplication, llfor division, and A for exponentiation.) Interval converging to a: = 1 II a: Interval converging to a: Interval converging to a: = 1