Concept explainers
Funding for NASA up to 1966 (Compare Exercise 51.) The percentage of the U.S. federal budget allocated to NASA from 1958 to 1966 can also be modeled by
(t is time in years since 1958).
a. Numerically estimate
b. How does your answer to part (a) compare with actual current funding for NASA?
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Finite Mathematics and Applied Calculus (MindTap Course List)
- 5x−12/x^2−x−42 has vertical asymptote(s) at x=arrow_forwardSketch the graph of ? = ?(? − 1)2⁄3. Find the followings if they exist a) the asymptotes b) the critical points c) the inflection pointsarrow_forwardThe following graph shows the approximate value V(t) of subprime (normally classified as risky) mortgage debt outstanding in the United States.arrow_forward
- In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product. T = −2n3 + 3n2 + n (a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units. (b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)T( )Calculate that value. (Round your answer to two decimal places.) thousand units(c) Find the approximate location of the inflection point. (Round…arrow_forwardq3.5 Find the following limits analytically or state that they do not exist.arrow_forwardlimit as x→−∞ 4/(e^x+7)=0 Enter the left-hand asymptote: y=arrow_forward
- A machinist is required to manufacture a circular metal disk with area 1000 cm2. (a) What radius produces such a disk? (Round your answer to four decimal places.) ?? cm(b) If the machinist is allowed an error tolerance of ±7 cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius? (Round your answers to four decimal places.) ?? cm < r < ?? cm (c) In terms of the ε, δ definition of lim x→a f(x) = L, what is x? area target radius radius target area tolerance in the area What is f(x)? 5 area target radius radius target area tolerance in the area What is a? area target radius radius target area tolerance in the area What is L? area target radius radius target area tolerance in the area What value of ε is given??? cm2What is the corresponding value of δ? (Round your answer to four decimal places.)?? cmarrow_forwardIn the function: f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?arrow_forward(a) What is wrong with the following equation? x2 + x − 12 x − 3 = x + 4 (x − 3)(x + 4) ≠ x2 + x − 12 The left-hand side is not defined for x = 0, but the right-hand side is. The left-hand side is not defined for x = 3, but the right-hand side is.None of these — the equation is correct. (b) In view of part (a), explain why the equation lim x → 3 x2 + x − 12 x − 3 = lim x → 3 (x + 4) is correct. Since x2 + x − 12 x − 3 and x + 4 are both continuous, the equation follows. Since the equation holds for all x ≠ 3, it follows that both sides of the equation approach the same limit as x → 3. This equation follows from the fact that the equation in part (a) is correct.None of these — the equation is not correct.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage