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a) Write the taylor series expansion about x = 0 for f(x) = ln(1+x). Include an expression for the general term.
b) Find the radius of convergence for the series in part a). Justify your answer.
c) Estimate the error in evaluating ln(3/2) by using only the first five nonzero terms of the series in part a). Justify your answer.
d) Use the result found in part a) to determine the logarithmic function whose Taylor series is the sum from n=1 to infinity of ((-1)^(n+1)x^2n)/(2n)
Find the temperature at 9:01 A.M.,at 9:08 A.M.,and at 9:20 A.m.
A representative is to be selected from each of 3 departments in a small college. There are 7 people in the first department, 5 in the second department, and 4 in the third department.
Let f(x,y) be an infinitely differentiable function. Suppose that Consider the surface z = f(x,y). Show that K(0,0) = f_xx(0,0) f_yy(0,0) - f_xy(0,0)^2.
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Express logarithm into exponential form and solve logarithmic equation and solve the log 4 2 = 1/2 in exponential form.
Independent events based probability. A company operates a telephone order system for a catalogue of its outdoor clothing products. The catalogue orders are processed in three stages. In the first stage, the telephone operator enters the order int..
Construct appropriate probabilistic models - appropriate probabilistic model and find the probability of getting doubles.
The professor counts his midterm as 2/3 of the grade and his final as 11/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put her average between 70 and 79 inclusive?
Show that the real part of the function z^(1/2) is always positive. Suppose f: G --> C ( C complex plane) is analytic and that G is connected. Show that if f(z) is real for all z in G, then f is a constant.
Identical twins must be the same sex, but the sexes of fraternal twins are independent. Find What is the probability of fraternal twins
Important information about Mixture, A tank contains 1320L of pure water.A solution that contains .o1kg of sugar per liter enters a tank at the rate 3L/min
Suppose that (a_n) ^ infinity, n=m is a convergent sequence of real numbers. Then (a_n) ^ infinity, n=m is also a Cauchy sequence
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