1. Express the sum 22 + 33 + 44 + 55 + ··· + 2121 using the sigma notation.
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2. Develop and evaluate
3.You must use the properties of the sigma notation.
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4. Evaluate (k + 3). You must use the properties of the sigma notation.
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5.Knowing that. Evaluate .
6. For which integer and positive value of not do we have that k = 105?
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7.Julie estimated that she would spend an average of $ 2000 per year on the purchase of broccoli over the next 15 years. She wants to determine the amountM which she would have in 15 years if, at the end of each year, she deposited this sum in a bank account bearing an annual interest rate of 3%. The mathematical formula to calculate this value is or R represents the annual deposit, i represents the annual interest rate and not the number of deposits made.
3. We construct a regular partition of the interval [-5, -1] defining not subintervals: - 5 = x0 < x1 < x2 < x3 < ··· < xk?1 < xk < ··· < xn?1 < xnot = -1.
(a) (3 points) Represent the surface graphically S delimited by the equation curve y = x2 over the interval [-5, -1].
(b) What is the larger of x?
4. Either f(x) and g(x) functions that can be integrated on R and such as
(a) (4 points) What is 3f(x) dx ?
(b) (4 points) What is
(c) (2 points) What is (f(x) + 3g(x)) dx ? Â Check that ln (3x2) is a primitive of 2/x
6. Evaluate the definite or indefinite integral.