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Scientific Research: 1983–2003 The number of research articles per year, in thousands, in the prominent journal Physical Review written by researchers in Europe during 1983–2003 can be modeled by
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Finite Mathematics and Applied Calculus (MindTap Course List)
- Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No 2. Yesarrow_forwardA company training program determines that, on average, a new employee can produce N( t) pieces of work per day after t days of on-the-job training, where N(t)=(87+42t)/t+6. Find lim s-9 N( t).arrow_forward1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/5arrow_forward
- lim y approaches 0 ................... [5y3 + 8y2]/[3y4 - 16y2]arrow_forward(b) Use your answers from above to determine lim t→0- (5t -1)/t. In your own work, you may want to add more values to the table from above. (d) Use your answers from above to determine lim t→0+ (5t -1)/t In your own work, you may want to add more values to the table from above. (e) Use your answers from parts (b) and (d) to find lim t→0 (5t -1)/tarrow_forwardevaluate the limit: limit of the square root of 1+t - square root of 1-t / t as t approaches 0arrow_forward
- (a) Use a graph to estimate the absolute maximum andminimum values of the function to two decimal places.(b) Use calculus to find the exact maximum and minimumvalues. f(x) =x - 2 Cos x, -2≤ x ≤ 0arrow_forward3. (a) Sketch the graph of a function that has one local minimum, two local maxima, and fourcritical numbers.(b) Sketch the graph of a function that has two local maxima, three local minimum, and noabsolute maximum.arrow_forwardIII) F HAS A LOCAL MAXIMUM AT (1/2 , 0)arrow_forward
- Find the absolute maximum and absolute minimum of the function f ( x ) = x 2 e -x on the closed interval [ 1 , 4 ].arrow_forwardThe cost C (in dollars) of producing x units of a product is C = 1.60x + 9,000. (a) Find the average cost function C. C = (b) Find C when x = 1,000 and when x = 10,000. C(1,000) =$ per unit C(10,000) =$ per unit (c) Determine the limit of the average cost function as x approaches infinity. lim x→∞ C(x) = Interpret the limit in the context of the problem. As more and more units are produced, the average cost per unit (in dollars) will approach $arrow_forwardLet G(x) = (x + 6)/(x2 + 4x - 12). a. Make a table of the values of G at x = -5.9, -5.99, -5.999, and so on. Then estimate limx--> -6 G(x). What estimate do you arrive at if you evaluate G at x = -6.1, -6.01, -6.001, .....instead? b. Support your conclusions in part (a) by graphing G and using Zoom and Trace to estimate y-values on the graph as x --> -6arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage