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- (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->9arrow_forwardwhat can be stated about the graph of f(x) given lim f(x)=2/3 x→−∞ a. f(x) has a horizontal aymptote aat y=2/3 b.f(x) has no horizontal asymptotes c.f(x) has no vertical asymptotes d.f(x) is discontinuos when x=2/3arrow_forwardFind the vertical and horizontal asymptotes. For the horizontal asymptotes you need to find the lim f(x) as x aproaches negative infinity and positive infinity f(x) = x/(x2-1)arrow_forward
- The limit lim x-> 0 e^x-1/x equals a derivative f' (c), for some function f(x) and some real number c. (i) find f(x) and c. (ii) Use the derivative of the function f(x) to evaluate the limit. (iii) Find an equaiton of the tangent line to y = f(x) at x = c, for the value of c you found in (i).arrow_forward1. 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. 0arrow_forwardThe graph of the function f(x)=cotxf(x)=cotx is given above for the interval x∈[0,2π]x∈[0,2π] ONLY.Determine the one-sided limit. Then indicate the equation of the vertical asymptote.Find limx→π− f(x)=limx→π- f(x)= This indicates the equation of a vertical asymptote is x= .Find limx→0+ f(x)=limx→0+ f(x)= This indicates the equation of a vertical asymptote is x=.arrow_forward
- lim xto1 of the function e(2^x) /(x^2) .. use L'Hoptial's Rulearrow_forward17.Let f(x)be a function such that limx→∞f(x)=∞ limx→−∞f(x)=7 limx→3+f(x)=∞ limx→3−f(x)=−∞ Determine the horizontal asymptote.y=Determine the vertical asymptote.x=arrow_forwardUse properties of limits and algebraic methods to find the limit, if it exists. lim x→−3 x2 − 9 x + 3 Step 1 We want to use properties of limits and algebraic methods to find lim x→−3 x2 − 9 x + 3 . Note that the function is a function. The numerator and denominator are 0 at x = , and thus we have the indeterminate form at x = . We can factor from the numerator and reduce the fraction. lim x→−3 x2 − 9 x + 3 = lim x→−3 (x − 3) x + 3 = lim x→−3 = − 3 =arrow_forward
- f(3) = 0 f has a horizontal asymptote at y = 2 f has vertical asymptotes at x = 4 and x = - 4 f(0) = 1 Create a functionarrow_forwardLet f(x)= 2x-2 if x<1 f(x)=x^2-1 if x is greater than or equal to 1 Evaluate Lim h-->0+ f(1+h)-f(1)/h Evaluate Lim h-->0- f(1+h)-f(1)/h Is the function f differentiable at a=1? Justify your answer.arrow_forwardLet f(x)=x^2−4/x^2−1 f′(x)=6x/(x^2−1)^2 f′′(x)=−6(3x^2+1)/(x^2−1)^3 (please enter response for that info above) a) Find all x- and y-intercepts and state the domain of the function. If there aren't any, state that there is none. b) Find the vertical and horizontal asymptotes of the function f(x). (Show all work using limits). c) Find the critical points of f(x). Find the open interval(s) where f(x) is increasing and the open interval(s) where f(x) is decreasing. If there aren't any of these, clearly state so. (show all work). d) State the x and y coordinates of any local maxima and local minima. If there aren't any, state that there is none. e) Find the open interval(s) where f(x) is concave up, and where f(x) is concave down. Find any inflection points. If there aren't any of these, clearly state so. (show all work). f) Sketch the curve, and label on your curve all the information found in part a - e.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage