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Zero average value Find the value of a > 0 such that the average value of the following functions over
53.
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Calculus: Early Transcendentals (3rd Edition)
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forwardAverage value Find the following average value. The average value of ƒ(x, y, z) = 8xy cos z over the points insidethe box D = {(x, y, z): 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, 0 ≤ z ≤ π/2}arrow_forwardAverage value Compute the average value of the following functions over the region R. ƒ(x, y) = e-y; R = {(x, y): 0 ≤ x ≤ 6, 0 ≤ y ≤ ln 2}arrow_forward
- _(5)^(\\\\infty ) Consider the function.\\n f(x)=x^(2) \\nCalculate the average value of f on the interval 3,7 . Give an exact answer.\\nAverage value:\\nDetermine c such that the average value of the function is equal to f(c) . Give an exact answer with no radicals in the denominator.\\n c=arrow_forwardFind the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = −sin x, [0, π] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.) x =arrow_forwardAverage value Compute the average value of the following functions over the region R. ƒ(x, y) = sin x sin y; R = {(x, y): 0 ≤ x ≤ π, 0 ≤ y ≤ π}arrow_forward
- Average value Compute the average value of the following functions over the region R. ƒ(x, y) = 4 - x - y; R = {(x, y): 0 ≤ x ≤ 2, 0 ≤ y ≤ 2}arrow_forwardFind the average value of the function over the given interval. (Round your answer to four decimal places.) f(x) = 9 − x2, [−3, 3] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to four decimal places.) x =arrow_forwardthe graph of f a) Evaluate the integral from 1 to 9 of f(x) dx (b) Determine the average value of f on the interval [1, 9]. (c) Determine the answer to part (a) when the graph is translated two units upward. Determine the answer to part (b) when the graph is translated two units upward.arrow_forward
- Average value Find the following average value. The average of the squared distance between the origin and pointsin the solid cylinder D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 2}arrow_forwardA cone that is constructed in such a way that the height is twice the radius. The measurement of the radius is found to be 23 inches, with a possible error of 0.03 inch. Use differentials to estimate the maximum error in the calculated volume of the cone where the volume is given by V = 2/3pi(r^3). Round answer to two decimal places. What is the relative error? What is the percentage error?arrow_forwardIntegration is not needed.a. Find the average value of ƒ shown on the interval[1, 6] and then find the point(s) c in (1, 6) guaranteed to existby the Mean Value Theorem for Integrals.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage