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1. Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b].
f(x) = 2 tan x, [0, π]
If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0.
2. Find the point on the graph of the function that is closest to the given point.
What will be the maximum revenue
A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery is 1/1000. Let x be the number of times you play the lottery before winning the first time. (a) Find the mean, variance, and standard deviation. Int..
Calculate the mass of the solid contained by the ellipsoid (x2/a2) + (y2/b2) + (z2/c2) = 1 given constant mass density β. Hint: You want to do TWO transforms.
The regression equation relating dexterity scores (x) and productivity scores (y) for the employees of a company is y=5.50 + 1.91x. What is the best predicted productivity score of 32.
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
If A and B are normal subgroups of G such that G/A and G/B are abelian, prove that G/(A intersect B) is abelian
A flagpole is tilted at an angle of seven degrees from he horizontal and towards the sun. It casts a shadow of 14 meters when the angle of elevation of the sun is 43 degrees. Find the length of the flagpole.
Pearson Brothers recently reported an EBITDA of $6.5 million and net income of $1.95 million. It had $2.21 million of interest expense, and its corporate tax rate was 35%. What was its charge for depreciation and amortization?
Suppose that you have 1800m of fencing with which to build three adjacent rectangular corrals. Find the dimensions so that the total enclosed area is as large as possible.
james believes the honor roll students at his school have an unfair advantage in being assigned to the math class they
Find residues of the function below at indicated points: [(cos z -1)/z]^2 z0 = 0
Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is first drawn from Box A and then another number from Box B. Using how many outcomes are in the event of getting both numbers even?
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