Concept explainers
1-4 Given that
which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible
(a)
(b)
(c)
(d)
(e)
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Calculus (MindTap Course List)
- Find limx2x24x2.arrow_forwardUse a graphing calculator to answer the following questions. a. From a graph of y=xex, what do you think is the value of limxxex?Support this by evaluating the function for several large values of x. b. Repeat part a, this time using the graph of y=x2ex. c. Based on your results from parts a and b, what do you think is the value of limxxnex, where n is a positive integer?Support this by experimenting with other positive integer n.arrow_forward3. Find lim f (x) where if r+3 f (x) = if r= 3arrow_forward
- 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim g(x) = L, but lim g(x) does not exist? If so, draw a sketch of such a x-2+ x-2 function. If no, explain why not.arrow_forward11. Consider the function f(x) - x³-ax²-x+b X+1 Given that f(a)= a-2 and the lim f(x) exists, determine all value(s) of lim f(x). X--1 X-1arrow_forwardA B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim /(x) = -3 x →-2 -5-4-3-2-1 Y -3- 2 -1, 1 2 3 4 -1 -2 -3 5 y = f(x) X ...arrow_forward
- 8. Sketch the graph of a function that satisfies the following conditions: lim f(x) = 1, lim f(x) = -2, x-0 f(0) = -1, f(3) = 1 lim f(x) = 2, X-3+arrow_forwardIf lim f(x) = 15 and lim g(x) = 25 then x5 x→5 lim[3 f(x)g(x) – 6] = x→5 O 1125 O 1131 O 30 O 195 O 1119arrow_forward1. Let f(x) = x²+x-6 |x2| 7 x b 2 + a 3 x - 2 if x 2arrow_forward
- 12. Give examples of functions f and g such that lim f(x)= lim g(x), but f(x) # g(x) for all x, including 0.arrow_forwardShow that if lim f(x) = lim h(x) = 3, and if f(x) < g(x) < h(x) for all x E (-1, 1), then lim g(x) = 3.arrow_forwardLet f(x) = Calculate the difference quotient x-4 f(1 + h) – f(1) h for h = .1 h = .01 h = -.01 h = -.1 f(1 + h) – f(1) lim h-0 harrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,