For the following geometric series, state the values of and. Then determine each indicated sum. Express your answers as exact values in fraction form and to the nearest hundredth
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Use the partial fraction command on your CAS to fin a convenient expression for the partial sum, and then use this expression to find the sum of the series. Check your answer by using the CAS to sum the series directly.
Attach the questions below
(1) Evaluate the integral
(2) Write out the form of the Partial fraction decomposition of the function, do not determine the numerical value of the coefficient.
(3) Write out the form of the Partial fraction decomposition of the function, do not determine the numerical value of the coefficient.
(4) Evaluate the integral (Remember to use absolute values where appropriate). Use C for the constant of integration.
(5) Evaluate the integral
(6) Evaluate the integral (Use C for a constant of integration).
(7) Evaluate the integral
(8) Make a substitution to express the integrand as a rational function and then evaluate the integral (use C as the constant of integration).
(9) Make a substitution to express the integrand as a rational function and then evaluate the integral (use C as the constant of integration)
(10) Find the volume of the resulting solid if the region under the curve from to is rotated about the x-axis.
(11) Find the volume of the resulting solid if the region under the curve from to is rotated about the y-axis.
2. The parts of this question are independent of each other. (a) Assume y is defined implicitly as a function of by the equation 2/5 + In(xy?) = 1. Solve for I when y=1 in this equation, and then evaluate at the point (1,1). [7 points) (b) Let y = V 2.0 (x - 2) Calculate the exact value of y' (4) and state your answer as a fraction in lowest terms. [8 points) IP +9
