Concept explainers
In Exercises 35–48 the graph of f is given. Use the graph to compute the quantities asked for. [HINT: See Examples 4–5.]
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Chapter 10 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
- Find the limit of the following: lim e(2/3-x) x→3+arrow_forwardIn Exercises 15 and 16, use the formal definition of limit to prove that the function has a continuous extension to the given value of x.arrow_forwardLet ƒ(x) = x^(1/(1-x)). a. Make tables of values of ƒ at values of x that approach c = 1 from above and below. Does ƒ appear to have a limit as x--> 1? If so, what is it? If not, why not? b. Support your conclusions in part (a) by graphing ƒ near c = 1arrow_forward
- Investigate the limit numerically and graphically. lim?→±∞8?+14?2+9‾‾‾‾‾‾‾‾√limx→±∞8x+14x2+9 Calculate the values of ?(?)=8?+14?2+9‾‾‾‾‾‾‾‾√f(x)=8x+14x2+9 for ?=±100,x=±100, ±500,±500, ±1000,±1000, and ±10000.and ±10000. (Use decimal notation. Give your answers to six decimal places.) ?(−100)=f(−100)= ?(−500)=f(−500)= ?(−1000)=f(−1000)= ?(−10000)=f(−10000)= ?(100)=f(100)= ?(500)=f(500)= ?(1000)=f(1000)= ?(10000)=f(10000)= Graph ?(?)f(x) using the graphing utility. ?(?)=f(x)= 8x+1√4x2+9 powered by What are the horizontal asymptotes of ??of f? (Give your answer as a comma‑separated list of equations. Express numbers in exact form. Use symbolic notation and fractions where needed.) horizontal asymptote(s):arrow_forwardGive a complete ?, ? proof of lim ?→3(4? − 5) = 7 That is, given ? > 0 find ? (as a function of ?) such that |?(?) − ?| < ? when |? − ?| < ?.arrow_forwardFind the following limits when they exist: 1. lim g(x) x to 3+arrow_forward
- Find the value of the postive constant c, such that lim x->infinty ((x-c)/(x+c))^x=1/4arrow_forwardUse L’Hospital’s Rule to find the limit.lim x → ∞ e^2x − e^−2x / ln(x + 1)arrow_forwardIn some cases, numerical investigations can be misleading. Plot f (x) = cos π x . (a) Does lim x→0 f (x) exist? (b) Show, by evaluating f (x) at x = ±12 ,±14 ,±16 , . . . , that you might be able to trick your friends into believing that the limit exists and is equal to L = 1. (c) Which sequence of evaluations might trick them into believing that the limit is L = −1.arrow_forward
- Note: You may need to assume the fact that lim M→+∞ Mne−M = 0 for all n.Sales of the text Calculus and You have been declining continuously at a rate of 2% per year. Assuming that Calculus and You currently sells 4,700 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. HINT [Use a model of the form Aert.]arrow_forwardA graphing calculator is recommended.For the limit lim x → 0 e2x − 1 /x= 2 illustrate the definition by finding the largest possible values of ? that correspond to ? = 0.5 and ? = 0.2. (Round your answers to three decimal places.) epsilon= 0.5 ? = epsilon= 0.2 ? =arrow_forwardsuppose f,g an d h are functions which g(x)<=f(x) <=h(x) ,for all x in an open interval containing a , except possibly at a. if lim g(x) ,x approaches to a does not exist or lim h(x) ,x approaches to a does not exist , will the lim f(x) ,x approaches to a do or does not exist ?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage