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- 12-Determine the equation of any asymptote and coordinate of holes forF(x)= -12x^3 +44x^2 -32x -16 / (3x^2 +7x+2) Please note that dont use the Lim's formulaFind the limit of lim((9+3x)1/2-3)/x as x approaches 01) Find the indicated limit if it exists. a) limx→0 squareroot x+4-2/x b) limx→−1.5 8x3+27/2x+3
- 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) for g(t)= t-9/square root t-3 . Make table of values with at least six appropriate inputs to evaluate the limits as t tends to 9. (b) make a conjecture about the value of lim t-9/square root t-3. t->91. 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. 0
- A. What is the vertical and horizontal asymptotes in the graph of y=f(x) what is the domain?1.Prove it by definition of limit. 2.find the horizontal asymptoteFind the limits to the following . (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) 1a. lim x->-∞ (6x^5-x)/(x^4+8) 1b.lim x->∞ 8cos(X) 1c. lim t->∞ sqrt(36t^2+5) -6t 1d. lim x-> ∞ (x^6+2x^9) 2. Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) y = (3x2 + x − 2)/ (x2 + x − 2)
- 9. Find the value of a such that exists and find the limit. limx-> -1 (2x2-ax-14)/(x2 -2x-3)Let ƒ(x) = (x^2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limxS -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,c instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as xS -3. c. Find limxS -3 ƒ(x) algebraically.Given limx→4f(x)=4limx→4f(x)=4 and limx→4g(x)=4limx→4g(x)=4, Evaluate : limx→4f(x)+g(x)8f(x). The Limit is ?