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- derivative of the given function keeping E fixed in terms of E and TThe circumference C of a circle is a function of its radius by C(r) = 2xr. Express the radius of a circle as a function of its circumference. Call this function r(C). r(C) = Preview Find r(187). r(187) = Interpret the meaning: O When the radius is 187, the circumference is r(187) O When the circumference is 187, the radius is r(187)Consider the functions f(x) = x and g(x) = sin x on the interval (0, ). (a) Complete the table and make a conjecture about which is the greater function on the interval (0, ). (b) Use a graphing utility to graph the functions and use the graphs to make a conjecture about which is the greater function on the interval (0, ). (c) Prove that f(x) > g(x) on the interval (0, ). [Hint: Show that h′(x) > 0, where h = f − g.]
- Suppose function fhas the graph as shown belowWhat is y(x) given that d²y dx² +4e-2x = 0 where you have the boundary conditions: dy dx y = yo (a constant) at You have to integrate twice as this is a second order differential equation so you need two boundary conditions to get the complete solution. (Most people are better at differentiating then integrating so check your answer by differentiating it!) = q (a constant) at x = 0 x = 0Please no written by hand solution