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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?Find the derivative of the function h(s) = 5 + 7/8s by limit process.Find the derivative of the function by the limit process. h(s) = −2 (square root of x)
- Solve for the derivative of the given functions using the Chain Ruleformula. Suppose f(x) = (sin(2x) + 1)7 .Find f′ (π/2) and f′(π). a.) What is What is f'(x) in the problem?b.) Which has bigger value between f′ (π/2) and f′(π)?8. Find the derivative of the following functions with respect to x by using either the product or the quotient rule, as deemed fit. Do Not simplify your final answer.(a) y = 10xe^ (−2x)(b) y = (1 + x) / (lnx)1. Determine the -values where relative extrema occur for y = (x ^ 2 + x - 12) ^ 2 . Use the second derivative test, if possible.
- 6) If y = f(x) has slope −4 at x = 3, and y value 5 at x = 3, a) write the formula for the tangent line to f(x) at x=3: b) estimate f(3.02) from the tangent line: c) If f is known to be concave up (S), is f(3.02) bigger than or smaller than your answer in b)?This questions has to do with marginal anyalysis in my price thoery economics class. We have to find the derivative of a function and find maximums and minimums. I know this question might seem simple, but I am just conceptually confused. If y = f(x) write down the FOC for a for a minimum is given by dy/dx=.2.2) Find the derivative of y with respect to T.