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- 17.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_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_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
- (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_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_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_forward
- lim xto1 of the function e(2^x) /(x^2) .. use L'Hoptial's Rulearrow_forwardThe 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_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
- 1. lim x-> -7 f(x)= 2. lim x-> -3 f(x) = 3. lim x->-2- f(x)= 4. lim x-> 1 f(x) = 5 lim x->3+ f(x) = 6. lim x->8 f(x) =arrow_forward3. Evaluate lim x→5 √x+4-3/ x-5. Show your complete solution. 4. Evaluate lim x→1 x-1/ √x-1. Show your complete solution. 5. Prove that lim t→-2 √1-t3/t +3/2 / t+2= 1/4. Show your complete solution.arrow_forwardF(x) = [x-1 when x<0, 1 when x = 0, x^2 - 1 when x>/= 0 For this function show that f(0) it not equal lim f(x) x-->0arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage