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MATH 126 Final: MATH 126 UW Final Exam Winter 2012 Solutions

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turquoisegnu128

31 Jan 2019

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Math 126 winter 2012: (a) t; (b) f; (c) t; (d) t; (e) t; (f) f; (g) f; (h) t; (i) f; (j) t. 2. (a) no. (b) 2x y = 0. 3. (a) (t) = (1 + 4 sin2 t)3/2 (b) r(t) = hsin t, 1 + cos t, 2 + 2 cos ti: the only critical point is (e, 1). It is a saddle point: x = 1 + 4t, y = 1 + 5t, z = 1 + 5t, the shortest distance is q 15. 8. (a) t3(x) = 2 + (x 1) + 2(x 1)2 1 (b) many correct answers. 3 (x 1)3: |f (x) t3(x)| . 6(1 a)3 . a4. (uses the fact that a 1. Two possibilities based on the answers in (b). a4: using the fact that 0 < 1 a < 1, show that |f (x) t3(x)| . Using the error bound |f (x) t3(x)| .

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Related Questions

Question1.

a)

Let L be the line containing thepoint P(2,-5,-1) and perpendicular to theplane 2x1+3x2+2x3=-3.

Find a vector equationfor L.

My answer: <2,-5,-1>+ t<2,3,2> (correct)

b)

At what pointdoes

Lintersect the yz-plane?

Question2:

x1 = -6 t - 4

x2 = - t+ 2

x3 = 5t - 6

and the second set ofparametric equations

x1 = 6t

x2 = ?

x3 = ?

describe the same line inR3. Find x2 and x3.

Question3:

It is one of 3 options foreach one: Parallel, perpindicular, or neither. Please explainwhy.

http://imgur.com/UbDuH8Z

Question4:

Find the point ofintersection of the two lines

a)

L1: x=1+t, y=-10-2t, z=-5-2t,

L2: x=7-4s, y=-10+2s, z=-7+3s.

Note that in general, twolines in 3D do not intersect. These two lines are carefully chosenso that they do

b)

Find the point where theline

x=1+2t,y=-4+t,z=-2-2t

intersects theplane

4x-y+3z=3.

Thanks. I have a lot ofpoints for this and will give it to someone that can helpme.

Please I need quick help these questions they are due so soon. Thanks

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pinkcrocodile662

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If U and V are positive constants, find all critical points of the function. (Enter your answers as a comma-separated list.) F(t) = Ue t + Ve -t t = Find all critical points of f(x) = 20 x 2 e - 0.3x and classify them as local minima of ,maxima. x = (smaller value) This critical point is a . x = (larger value) This critical point is a . Consider f(x) = x 8 (7 - x) 9. Find f '(x) and simplify your answer. f '(x) = Find all critical points of f(x) and then use the first derivation test to determine local maxima and minima. f(x) has a at x = (smallest value) Local Maximum OR Minimum OR Neither f(x) has a at x = Local Maximum OR Minimum OR Neither f(x) has a at x = (largest value) Local Maximum OR Minimum OR Neither Find the inflection points of f(t) = t 4 + t 3 - 18t 2 +8. Give exact answer. t = (smallest value) t = (largest value) Sketch a possible of y = f(x), using the given information about derivation y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x. Let f be a function f(x) > 0 for all x. Let g = 1/f. If f is increasing in an interval around x 0, what about g? g is increasing in an interval x 0. g is zero in an interval around x 0. g is decreasing in an interval around x 0. We cannot tell whether g is increasing or decreasing in an interval around x 0. g is constant in an interval around x 0. If f has a local maximum at x 1, what about g? g has a local maximum at x 1. g has both a local minimum and a local maximum at x 1. We cannot tell whether g has a local minimum or a local maximum at x 1. g has an inflection point at x 1. g has a local minimum at x 1. If f is a concave down at x 2, what about g? g is increasing at x 2. g is flat at x 2. We cannot tell whether g is concave up of concave down at x 2. g is concave down at x 2. g is concave up at x 2. You are given the graph of the second derivation function f" below. Which of the given have x-values that are inflection points of the function f? (Select all the apply.) A B C D E F G H I none of the above