27. (1 point) If x"(1) = -10, x'(1) = 0 and x(1) = 6, then x (1 ) =_ 28. (1 point) If s" (1) = - 72's -2, s'(1) = 1 and s(1) = 0, then x (1) S' ( 1 ) =_ Answer(s) submitted: s (1 ) =_ Answer(s) submitted: (incorrect) (incorrect) Generated by WeB Work, http://webwork.maa.org, Mathematical Association of AmericaRex Wu S22M171 Assignment PQ Exam3_Optional due 04/11/2022 at 08:00pm MDT V4 + 0.1 ~ 1. (1 point) Compute the first derivative of each of the following func- Answer(s) submitted: ions: (a) P(1) = 2' P' (1) =. (incorrect) (b) E( ) = >In(1 +e") E'(y) = 5. (1 point) (c) 1(w) = sinh(cos(w)) [Note: This is just w.] You want to calculate the depth of a fissure on Mars from the I'(w) = equation s(t) = 412 by timing how long it takes a heavy stone (d) k(x) = In(7x2+ 2x+ 1) you drop to hit the ice below. K (x ) = Here s(t) is the distance in meters an object falls in t seconds under the influence of gravity on Mars. Suppose you measure (e) q(x) = = In(x) Itx the time to be 5 seconds. 9' (x) = Use differentials to estimate the error in depth if there is a 0.1 (f) 8(1) = cosh(at2 + b) second inaccuracy in measuring the time. 8' (1 ) = Error in depth ~ (g) g(1) = sinh(41 + 2) 8 (1) = Answer(s) submitted Answer(s) submitted: (incorrect) . . . . 6. (1 point) I the linear approximation for h ~ 0 for W w (h) = (1 + h/R) 2' incorrect which is the weight of a body at altitude h above the earth's sur- 2. (1 point) Find y using logarithmic differentiation of face, where W is the weight of the body at the surface of the y = xcos(xx) earth and R is the radius of the earth. L(h) = y Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 7. (1 point) 3. (1 point) Find y using logarithmic differentiation of The quadratic approximation to a function f(x) at x = a is given by y = (2x+ 1)* Answer(s) submitted: 2 ( x) = f(a) + f' (a) (x - a) +@(x-a)?. Find the quadratic approximation to f(x) = e" at x = 0. (incorrect) e(x) = 4. (1 point) Use it to approximate Find the linear approximation to vb + x for x near zero. 20.05 ~ Here b is a positive constant. L( x ) = Answer(s) submitted: Use your approximation to estimate(incorrect) 13. (1 point) f" (x) = 2 - 6 x 2 (x 2 + 1 ) 3 Multiple Choice. Suppose that f"(x) 0 for x > - 2, (incorrect) f" (x) > 0 forx 0. In general, a lapse rate is the negative of the rate of tempera- ture change with altitude change, thus: dT 16. (1 point) Y = dz Sketch the graph of a continuous function for which where y is the lapse rate given in units of temperature divided f"(x) 0 everywhere else. If the lapse rate exceeds 7'C / km in a layer of the atmo- sphere, it is favorable for thunderstorms and tornado formation 17. (1 point) If concurrent measurements indicate that at an elevation of 6 km, the temp is -20'C and at 3 km the temp is 10 C, can you Given that f(x) = 2+ 1' conclude that the lapse rate exceeds the threshold value of 7C 2x at some intermediate elevation? [?/Yes/No]. f (x ) = T, ( x 2 + 1 ) 2 , and Explain. Start with