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Finite Mathematics and Applied Calculus (MindTap Course List)
- 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) Use the Trapezoid Rule to estimate the following integral. Use n=5 integral of (e^(x^2)) dx from 0 to 1 b) Use the Error Bound Formula for the Trapezoid Rule to find a best estimate for the error involved in part aarrow_forwardEvalulate the integral. (Use C for the constant integration.)arrow_forward
- New York students must attend t hours, where t ∈ [0,H], of lectures and pass two quizzes to be in good standing for their examination. The number of students who attended between t1 and t2 hours of lectures is described by the integral shown in the image below. As a result of COVID-19, some students attended less than H/2 hours of lectures before the college was closed down and passed the quizzes so they are qualified to take the examination.The final score each student got is proportional to the amount of lectures he/she had attended which is given by the functionL(t)=(100/H)tWhat was the average in the class?arrow_forwardUse the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) The integral from 2 to three of the the square root of x^3 -8 dx, n = 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rulearrow_forwardA company models income, measured in thousands of dollars, using the continuous stream f(t)=200|tln(t)| for t>0, where t is measured in years. What is the total revenue generated in the first two years? Give your answer in thousands of dollars. When giving your answer, use numbers only. Do not include the dollar symbol, commas or anything to denote thousands in your answer. Hint: You may use the fact that the integral of a product of two functions can often be calculated using the formula ∫uv′dt=uv−∫vu′dt, where v′ denotes the derivative of v, and u′ denotes the derivative of u. You may also use the fact that t2ln(t)→0 as t→0.arrow_forward
- Apply u-substitution to determine the following integralsarrow_forwardF function [0,136] continous and every t is part of [0,136] for F(t) > 0 . What is the value of this integral ?arrow_forwardUse u- substitution to find the integrals: A.) integral x sqrt(x+1)dx B.) integral x e^(x^2)dxarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning