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Calculus Volume 3
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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_forwardA soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.arrow_forwardHow can I help you? use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02) given g (x, y, z) = ze2" y + cos(xz – 3)arrow_forward
- Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1 f(x)dx and the value 3 for n=4, what is the value of b?arrow_forwardThe temperature at a point (x,y,z) is given by T(x,y,z)=1200e-x^{2}-2y^{2}-z^{2} where T is measured in ∘C and x, y, and z in meters.arrow_forwardTest for exactness of the DE using ∂M/∂y and ∂N/∂x 2xy − 9x2 + (2y + x2 + 1)y′ = 0.Show complete solution.arrow_forward
- What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)? Answer in rectungalur formarrow_forwardFrom the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2, y' = 2, obtain the value of y' at x = 2. Answer: 0.865arrow_forwardThe temperature at a point (x,y,z) is given by T(x,y,z) = 1300e^(-x^2-2y^2-z^2) where T is measured in C and x, y, and z in meters.arrow_forward
- Using integrating factors found by inspection ydx + 2(y4 − x)dy = 0 y(x3exy-y)dx + x(y + x3exy)dy=0 2x5y' = y(3x4+y2)arrow_forwardA cylindrical pool that has a 3.3 meter radius and is 1.8 meter deep. v=πr2v=3.14(3.3)(1.8)=18.6156m3 Find all errors in this equation. There are several. Correct the work.arrow_forwardTest for its exactness to obtain the general solution or particular solution if possible. 3y(x2 −1)dx+(x3 +8y−3x)dy= 0 when x= 0, y=1arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning