Concept explainers
(a) Evaluate h(x) = (tan x – x)/x3 for x = 1, 0.5, 0.1 , 0.05, 0.0 1, and 0.005.
(b) Guess the value of
(c) Evaluate h(x) for successively smaller values of x until you finally reach a value of 0 for h(x). Are you still confident that your guess in pan (b) is correct? Explain why you eventually obtained 0 values. (In Section 4.4 a method for evaluating this limit will be explained.)
(d) Graph the function h in the viewing rectangle [–1, 1] by [0, 1]. Then zoom in toward the point where the graph crosses they-axis to estimate the limit of h(x) as x approaches 0. Continue to zoom in until you observe distortions in the graph of h. Compare with the results of pan (c).
Trending nowThis is a popular solution!
Chapter 2 Solutions
Calculus: Early Transcendentals
- 2. Find lim x - sin x x → 0 x – tan xarrow_forward(a) Evaluate h(x) tan(x) - x for x = 1, 0.5, 0.1, 0.05, 0.01, 0.005. (Round your answers to six decimal places.) h(1) h(0.5) = h(0.1) h(0.05) h(0.01) h(0.005) =| (b) Guess the value of lim ane=x. (If an answer does not exist, enter DNE.)arrow_forwardConsider the following function and graph. 1 f(x) x + 2 3 1. Determine whether f(x) approaches co or -co as x approaches -2 from the left and from the right. (a) lim f(x) x→-2 (Ь) lim f(x) メ→-2"arrow_forward
- 2. -7 -6 -3 3 4 -2 -3 %24arrow_forwardQ2:- Evaluate the magnitude tan (2x) 1. lim-arrow_forwardEstimate the value of Lim x -> 0 (sin x) / (sin π x)By graphing the function f(x) = (sin x) / (sin π x).State your answer correct to two decimal places. Check your answer in part (a) by evaluating f(x) for values of x and approach to 0.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,