OC userin Mathematics·13 Dec 2017(4) Find the equation of the tangent line to xy2 + ex+y = cos(xy) at the point (0,0). (A) y = x (B) y=0 (C) y = -2 (D) y= -2.c (E) None of the above.
OC userin Mathematics·13 Dec 201718. Suppose h(t) = 100(2.05)* + ln(t). (a) (8 points) Determine l'(t). You do not need to simplify the derivative. (b) (4 points) Determine the equation for the line tangent to h(t) at t = 1. Approxi- mate values to two decimal places.
OC userin Mathematics·13 Dec 20172. Evaluate the following limits. (Do NOT use L'Hospital's Rule.) · cos(TTC) [1] (a) lim 11+1 Solution: By the Continuity Theorems we have [2] (b) lim 1r| tan- ( Solution: We know that - *
OC userin Mathematics·12 Dec 20179. Let f(0) = 2.1 + cos.r. [3] (a) Using appropriate theorems, prove that f(1) = 0 for some r in the interval [-/2,0). [3] (b) Show that f(0) = 0 has exactly one solution. [3] (c) If g is the inverse function of f, find g(n) and g'().
OC userin Mathematics·11 Dec 2017PROBLEM 07: A contest winner gets to pick their prize by selecting three DVD's from a list of 10 different DVDs. How many different prizes are possible? A) 120 B) 720 C) 30 D) 6 E) none of the above
OC userin Mathematics·11 Dec 201713. The improper integral A) equals - B)equals C) equals D) diverges to o E) diverges to -
OC userin Mathematics·11 Dec 20172 – 9.2 7. Consider the function p(t) = 7 4.(x+3)(2x – 7) (a) Find the domain of p(t)
OC userin Mathematics·10 Dec 20171 , 2. If u = (1, -1, 3) and v = (2,1, -1), find u x v. A: (2, -1, -3) B: (-2, -7,3) C: (-2,7,3) D: (-3,7,3) E: (-3,5,4)
OC userin Mathematics·11 Dec 2017The ma 1 i 11 [10] 7. Let A = 0c 0 where ce R is constant. For what values of cis A diagonalizable? 1 0 1 Justify your answer. 1-measures Hola sortie
OC userin Mathematics·10 Dec 2017[3] 5. (a) Let f(T) = 1 + Write the Riemann sum for f over the interval (0, 1) using a uniform partition of (0,1) into 5 equal subintervals and mid-points as your sample points. There is no need to simplify your answer. [3] (b) If f is the function defined by f Jo 2 + sint dt, find f'(2). (c) Sketch the region in the first quadrant bounded by: y==y= VT, 1=1, r=e, and then find its area.
OC userin Mathematics·10 Dec 201713. A student has 3 volumes by K. Marx and 5 movies with the Marx brothers. His evening schedule consists of watching a movie, then studying one of the Marx volumes, and then again watching a movie, different from the first. How many different evening schedules are there? (A) 13 (B) 30 (C) 3C(5,2) (D) 60 (E) 12 (F) none of the above
OC userin Mathematics·11 Dec 20172. (8 points) Is the following function f[] continuous for all real r? For full credit, you must clearly justify your answer. if r <3, f [1] = Vx+1 -2 2-3 , ifr> 3