cliffton m. fischbach|if f(x) = x^2 +10 sin x, show that there is a number c such that f (c ...,natasha nice

Let x be the length (in in.) of the side of the square at each corner. x = in. (Round your answers to two decimal places, if necessary.). Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. f (x) = (b) State the domain of this function. (Enter your answer using interval notation.)

The temperature f(t) of the body at time t in hours after being introduced to an environment having constant temperature T 0 is f(t)=T 0 +Ce-kt where C and k are constants.. A cup of coffee with temperatures 125 degree F is placed in a freezer with temperature 0 degree F.

As we are evaluating from 0 to 4, x will be evaluated at 4i/n for i = 1 to n. f(x i) = (4i/n) 2 /3 - 6. ∑ 1 n 4/n ((4i/n) 2 /3 - 6) =. 4/n ((16/(3n 2)n(n+1)(2n+1)/6 - 6n) = 64/9 + 32/(3n)+ 32/(9n 2)- 24= -152/9 + 32/(3n) + 32/(9n 2). The limit as n goes to infinity is -152/9

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