{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math 100 Dec 05 Questions

Math 100 Dec 05 Questions - (h(i(j(k December 2005 Math...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (h) (i) (j) (k) December 2005 Math 100/180 Final Exam Evaluate hm m. x—r9 f1? — 9 Calculate and completely simplify the derivative of f(a:) 2 In (1000 tan—1(m)). [Note 1 Another notation for tan‘ is arctan]. Find an equation of the line tangent to the graph of 3:3 + 3/3 = 35334 at the point (x,y) : (3/2, 3/2). Find the second derivative of g(m) = sin (621). If we expand sin2(z) in a Maclaurin series, say sin2(x) = Z” cnz", find c6. [Hint sin2(x) = %(1— cos(2a:))]. ":0 Find f’(:r) if = (sin Suppose we know that f(1) = f’(1) : 1. Define g(x) = f(x3). Use a linear approximation to the function 9 (not a linear approximation to the function f) to estimate g(1.1). Use a suitable linear approximation to the estimate (17)1/4. Give your answer as a fraction with integer numerator and denominator. What does Taylor’s Inequality give as an upper bound to the error in part (h)? Using Newton’s Method, starting with $1 = 2, find the approximation 16;; to the root of the equation 20m — m3 — 24 = 0. A particle moves in a straight line so that its velocity at time t is v(t) = If its position at time 9 is 5(9) 2 20, find 3(10). ' 2. A circular ferris wheel with radius 10 metres is revolving at the rate of 10 radians per minute. How fast is a passenger on the wheel rising when the passenger is 6 metres higher than the centre of the wheel and is rising? Include units in your answer. \ passenger ground 3. Wallapak stores her malt beverages outside her house, on her back porch. On a very hot day, she takes one such beverage and places it in her refrigerator, which is constantly kept at 4°C. After 15 minutes, the beverage cooled down to 26 °C, and, after another 15 minutes, it was at 15°C. How hot was the beverage when it was placed in the refrigerator? Assume the temperature of the beverage obeys Newton’s Law of Cooling. . Find the derivative of f(:r) ; x/l — 2m using the definition of derivative. No credit will be given for using differentiation rules, but you may use differentiation rules to check your answer. 5. Let f($) 2 (a) Determine all of the following if they are present: critical numbers, :r—coordinates of local maxima and minima, intervals where f is increasing or decreasing; m—coordinates of inflection points, and intervals where is concave upwards or down- wards; (iii) equations of any asymptotes (horizontal, vertical, or slant). (b) Sketch the graph of y = f (at), giving the (at, y) coordinates for all points of interest above. Draw your sketch on the back of the previous page. 6. At noon, a sailboat is 20 km due south of a freighter. The sailboat is traveling due east at 20 km/h, and the freighter is traveling due south at 40 km/h. (a) When are the two ships closest to one another? Remember to justify your answer. (b) If the visibility at sea is 10 km, could the people on the two ships ever see each other? 7. (a) A function is defined to equal cos(ax) + b for w 2 0 and 2 — x3 for m < 0, where a and b are constants. It is known that this function is differentiable everywhere. Find all possible values for a and b. (b) A function g(x) satisfies g(0) = 0, 9(1) 2 1, and 9(2) 2 —1. It is known that this function is twice differentiable everywhere (i.e. g”(:r) exists for all Prove that g’(c) : 0 for some real number 0. Give complete justification, specifying any relevant theorems. The End ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern