OC userin Mathematics·17 Dec 20173 21. There are 3 white balls and 4 black balls in an urn. Balls are drawn from the urn at marks random, one by one without replacement, until a black ball is drawn. (a) Draw a probability tree which models this stochastic process. Be sure to put appro- priate probabilities on all branches. (b) What is the probability that eractly 3 balls will be drawn? DO NOT SIMPLIFY YOUR ANSWER.
OC userin Mathematics·17 Dec 2017[1] 1. (a) Solve 2 – 31 < 7. Solution: We have – 7 0 on (-0, 1] U [2,). Next, we need to see where Vr2 – 3r +2 -1 > 0. If r2 - 3.c + 2 – 1 > 0, then V.22 – 3.0 +2 > . Observe that this is definitely true if r < 0. If r > 0, then squar- ing both sides we get 22 - 3.+2 > 1 2 > 3. V A VICO Thus, the domain of f is (-00, ). [2] (c) Find the exact value of tan(sec-14). Solution: Let y = sec-14. Then, sec y = 4. From the diagram we get that tan(sec-? 4) = tan y = 15 [2] (d) Find all r such that sin(2.x) = COS I. Solution: We have 2 sin r cos r = COS I, SO 0 = 2 sin Cos I -Cos I = cos .r (2 sin c - 1). Hence, sin(2x) = cost when cos x = 0, or when sin r = Thus, r= +ik, kez, I= +2nk, ke Z, or r= +2nk, kez [2] (e) State the precise mathematical definition of lim f(x) = 0. Solution: For every e > 0 there exists a 8 >0 such that if 0 < x-al
OC userin Mathematics·17 Dec 20175. Find the equation of the circle with center at (2, -1) and going through the point (5, 4).
OC userin Mathematics·16 Dec 20173. Find the equation of the line tangent to the curve 2x²y + y2 - 6x - 9 = 0 at the point (1,3).
OC userin Mathematics·16 Dec 201714. How many critical points does f(x, y, z)=2x' + xy+ y2 +100-z(x + y-100) have? A) exactly one B) none C) exactly 2 D) exactly 3 ) none of these
OC userin Mathematics·14 Dec 20178. Two men start moving from the same point. One travels south at 6 km/h and the other travels west at 2 km/h. At what rate is the distance between the two men increasing one hour later?
OC userin Mathematics·16 Dec 20173x - 5 is the slope of the tangent line (f) At how many points on the graph of y = f(x) = equal to 1?
OC userin Mathematics·15 Dec 20171. Let f(x) = x2. Find f'(x) from first principles, i.e., by using only the definition of the derivative.
OC userin Mathematics·15 Dec 2017Contains Verified Answer5. If f(x)= 27° -5x + 3x –7 then A) lim f(n= f(x)=0 B) lim f(x)=0 D) lim f(x)=-- C) lim E) None of these
OC userin Mathematics·16 Dec 20177. If lim f(x) = 3, lim g(x) = -2, and lim h(x) = 4, evaluate the limit (C) 13 (A) -1 (D) 5 (B) 3 (E) 7
OC userin Mathematics·14 Dec 201713. If y' = e*- and y0) = in 2 then = - © y= In (e* +2) Dy=3+ In 2 y = In (e* +1)
OC userin Mathematics·13 Dec 20174. Consider the following two subsets of R2: A=[0, 2] x [0, 2] and B=(-1,1] x [-1,1]. Draw the sets A, B, A B and A - B in the plane. Use a solid or a dotted line to indicate whether the boundary is or is not part of the set. AnB A-B
OC userin Mathematics·14 Dec 20175. Evaluate the following two definite integrals. 1 + 15.4 dr. Simplify your answer as much as you can. [7 points) (b) (2xe3e dr. Simplify your answer as much as you can. [9 points)