Hi, Here's yet another problem: Let fn(x)=(sin(nx))/n2. a) Show that the series sigma fn(x) for all x but the series of derivatives sigma f'n(x) diverges when x=2n(pi), where n is an integer. b) For what values of x does the series sigma f''n(x) (the second derivatives) converge? As you can tell, this is differentiation and integration of a power series. I only got as far as proving that fn(x), but the rest is very confusing. Thanks!
Hi, Here's yet another problem: Let fn(x)=(sin(nx))/n2. a) Show that the series sigma fn(x) for all x but the series of derivatives sigma f'n(x) diverges when x=2n(pi), where n is an integer. b) For what values of x does the series sigma f''n(x) (the second derivatives) converge? As you can tell, this is differentiation and integration of a power series. I only got as far as proving that fn(x), but the rest is very confusing. Thanks!
Hi, Here's yet another problem: Let fn(x)=(sin(nx))/n2. a) Show that the series sigma fn(x) for all x but the series of derivatives sigma f'n(x) diverges when x=2n(pi), where n is an integer. b) For what values of x does the series sigma f''n(x) (the second derivatives) converge? As you can tell, this is differentiation and integration of a power series. I only got as far as proving that fn(x), but the rest is very confusing. Thanks!
a) Show that the series sigma fn(x) for all x but the series of derivatives sigma f'n(x) diverges when x=2n(pi), where n is an integer.
b) For what values of x does the series sigma f''n(x) (the second derivatives) converge?
As you can tell, this is differentiation and integration of a power series. I only got as far as proving that fn(x), but the rest is very confusing.
Thanks!
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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