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âv = (6, 4) and âw = (2, â1)
a) Find a value of k so that |k( âw + 1/2 âv )| = â 13
b) Find âk using your value for k from the previous problem. What is | â k( âw + 1/2 âv )|?
â = Vector
A function f[x] is defined by the power series x/2 + x^2/12 + x^3/240 + x^4/10080 + ⦠+ (k x^k)/(2 k)! + â¦
In other words, x/2 + x^2/12 + x^3/240 + x^4/10080 + ⦠+ (k x^k)/(2 k)! + ⦠is the expansion of f[x] in powers of x.
What is the exact value of f[0]?
Find convergence intervals for each of the following power series. Use the Power Series Convergence Principle directly, use the ratio test, or use any other method you like.
1 - x/2! + x^2/4! - x^3/6! + ⦠+ (-1)^k (x^k/(2 k)!) + â¦
â1 - 2^3 x + 3^3 x^2 - 4^3 x^3 + ⦠+ (-1)^k (k + 1)^3 x^k + â¦â