# Search results

1. ### Convergence and the Alternating Series test

Is this a homework question? If so, it should be posted in the homework section, and you should show what you have done so far, and people will give you hints or help.
2. ### Numerical analysis(Bisection Method)

Taking the derivative just guarantees that you can easily find a minimum or maximum of the function. It helps most when it's not that obvious where a function is below or above zero. It doesn't matter that it's a parabola, and you can do it equally by guessing, plotting the function, or other...
3. ### Getting Residues Complex Analysis

Hi. The formula for the residue of a function at z_0, a pole of order n is: res(f;z_0) = \lim_{z \rightarrow z_0} \frac{1}{(n-1)!} \frac{d^{n-1}}{dz^{n-1}} (z-z_0)^n f(z) Here the factorial term is just 1! = 1. So what we need is the derivative of (z-z_0)^2 f(z) . So we get...
4. ### Numerical analysis(Bisection Method)

a and b don't have opposite signs (necessarily), the function evaluated at those points has opposite signs. Now you can choose any points you want, as long as they satisfy that condition. In this case, you have a parabola. So one way to find points that will be suitable is to take the...
5. ### Bound on Taylor Series Error

http://en.wikipedia.org/wiki/Taylor%27s_theorem#Estimates_of_the_remainder
6. ### Can the limits of a function be imaginary?

The limit of a function at a particular point can be an imaginary number...but only if the function is complex-valued. A function is a map from one space to another. The functions commonly encountered in introductory calculus courses are normally real-valued functions, which take a single...