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- For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant. 30. Find the local minimum of the function graphed in Exercise 27.Find a formula for a function that has vertical asymptotes x =1 and x = 3and horizontal asymptote y =1 .Investigate lim (1 + x) 1/x numerically and graphically. x➔0
- Draw a graph where limx→2f(x) exists but f(x) is discontinuous at x = 2. Name the type of discontinuitythat has this propertyFind the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the definition: m=lim->a f(x)-f(a)/x-a 2)using the equation: m=lim->0 f(a+h)-f(a)/hThe percent of research articles in one prominent journal written by researches in the Unites States during 1983-2003 can be modeled by A ( t ) = 12 + 28/1+.6(1.6)-t where t is time in years since 1983. Numerically and/or graphically estimate lim x → ∞ A ( t ). (Do not include units or symbols.)
- Find the limit of the function lim x → − 6 ( 2 x + 12 | x + 6 | )1. Your friend from Calc 2 says that the following statement is not true: x2-x-2/x-2 = (x+1) She is right, the two functions involved are not exactly the same. a) What is different? Answer with complete sentences and supporting graphs. b) Now consider the following equation, which is true: lim x approaches 2 x2-x-2/x-2 = lim x approaches 2 (x+1) How does adding a limit sign in front of each function solve the problem from part a?Find limit (a) by investigating values of the function near the point where the limit is taken and (b) by using a graphing calculator to view the function near the point.