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Please solve the following with as much explanation of each step as possible.
Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(c) = 0. Find an interval for the function g over which Rolle's theorem can be applied, and find the corresponding critical number of g (k is a constant).
(a) g(x) = f(x) + k
(b) g(x) = f(x-k)
(c) g(x) = f(kx)
Four congruent quarters circle are drawn inside square of side length four centimeters f ind the shaded area
Let X be a path-connected space and suppose that every map f: S^1 --> X is homotopically trivial but not necessarily by a homotopy leaving the base point x_0 fixed. Show that pi_1(X,x_0) = 0.
Flying with the jetstream, the same jet travels 4600km in 4 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?
There are two small cities, Santa Clara and Santa Rosa. Santa Clara has 20 houses and Santa Rosa has 15 houses. An inspector must randomly choose 5 houses in Santa Clara and 7 houses in Santa Rosa to inspect.
Suppose that X1=-1, x2=2, x3=4, x4=-3 is a solution of a non-homogeneous linear system Ax = b and that the solution set of the homogeneous system Ax=0 is given by the formulas:
How do you explain why vectors QR and RQ are not equivalent? Explain when the elimination method for solving a system of equations is preferable to the substitution method.
Finding the side lengths of the given triangle - Evaluate the vertices of the triangle such that its area is a minimum.
Find the probability of having no more than three boys
Using graphing to check your answers is helpful. When you factor a trinomial into two binomials, each binomial represents a linear relationship. If you plot the two binomials (which are just lines) on a graph
Please solve for the following: Find a particular solution to, Solve: A Second Order ODE y'' + 5y' +4y = -13te^(3t)
Given the adjacency relation p = {(1,4), (1,5) (1,6), (6,2), (6,3), (6,5)} on the set N ={1,2,3,4,5,6}, find the corresponding directed graph and adjacency matrix.
At the 0.01 level of significance, test the claim that the mean reading times lour the lour age groups are equal.
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