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How would you find the definite integral for the following functions:
a. f(X) = 67 over the interval [0,1]
b. f(X) = 30X over the interval [0,2]
c. f(X) = 2- X2 over the interval [2, 4]
d. f(X) = 2- X2 over the interval [3, 4.5]
e. f(X) = 12- 2X over the interval [0, 1]
f. f(X) = X3 + X4 over the interval [0, 3]
g. f(X) = 50X - X2 + X10 over the interval [0, 1]
A particle's position is give by s = 3t^3 - t^2 + 2t. What is it's acceleration at t=2? This seemed too easy.
If F is a field, prove that the field of fractions of F[[x]] is the ring F((x)) of formal Laurent series. Show that the field of fractions of the power series ring Z[[x]] is properly contained in the field of Laurent series Q((x)).
Integrate the integral below using the partial fractions method. (S represents the sign for integration) S x^3 + 4 / (x^2 - 1)(x^2 + 3x + 2) dx
Suppose that derivative of the function f is given by f'(x) = 3x and suppose that the point (4,2) is on the graph of f. Write an equation of a line tangent to the graph of f at the point (4,2)
Derivative of the natural logarithm by using the fundamental theorem of calculus - Evaluate the derivative of y = ln x. This solution below is not complete.
In a ring R, an idempotent is an element x ? R such that x * x = x (where * denotes the ring multiplication). Show that if R is an integral domain, then R has exactly two idempotent elements.
Compute the mean and variance for binomial distribution. Calculate the mean and standard deviation (by hand) for the binomial distribution with the probability of a success being 1/4, 1/2, 3/4.
A brief and an original writeup has been provided to explain the student community the concept of vertical lines. A graphical example of equation x=4 has been attached to aid the understanding of the concept.
The acceleration due to gravity near the surface of Mars is 3.72ms^-2. A rock is thrown straight up from the surface with an initial velocity of 23ms^-2.
What is the probability that a random sample of 50 such women will yield a mean entry-level that exceeds $58,000?
The instructions are as follows: write each equation in slope-intercept form and then find the slope and y-intercept.
What is the maximum possible area of a rectangle inscribed in the ellipse x2 + 4y2 = 4 with the sides of the rectangle parallel to the coordinate axes?
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