16. The graph of g has a vertical asymptote at x = 2 and horizontal asymptotes at -1 and y = 3 (see figure). Determine the following limits: lim g(x), lim g(x), lim g(x), and lim g(x). x→2- x→2+ y A 6+ y = g(x) 4+ 2- 4 -2- -4
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Determine the following limits at infinity. PLEASE USE LIMITS, NOT DERIVATIVES.
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- Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 01.Prove it by definition of limit. 2.find the horizontal asymptote
- Let ƒ(x) = (3^x - 1)/x. a. Make tables of values of ƒ at values of x that approach c = 0 from above and below. Does ƒ appear to have a limit as x --> 0? If so, what is it? If not, why not? b. Support your conclusions in part (a) by graphing ƒ near c = 0.A tank contains 1300 L of pure water. The solution that contains 0.01 Kg of sugar per liter enters the tank at the rate of 7L/min. and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the beginning? y(0)= to( Kg (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) As t becomes large what value is y(t) approaching? in other words, calculate the following limit lim t-oo y(t)= (kg)Prove that x=-1 and x=1 are vertical asymptotes, and that the x-axis is the horizontal asymptote of y=coth-1x by graphing.
- a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=The graph shows a rough representation of the aggregate market depth of the stocks comprising the S&P 500 on the say of the US stock market crash at 2:45 pm on May 6, 2011, the flash crash. t is the time of day in hours and m(t) is the market depth in millions of shares. a. Compute the following (if a limit does not exist say why) lim m(t) t approaching 14.75 to the left lim m(t) t approaching 14.75 to the right lim m(t) t approaching 14.75 m(14.75) b. What do the answers to part a tell you about the market depth?