Exponent Definition and 212 Threads

Hi all, I've been trying to get back into mathematics by teaching myself calculus. I've been starting with the book "Calculus Made Easy" and have been doing fine except for one little thing I encountered on page 57. He shows a mathematical proof of why the derivative of y = x^\frac {1} {2}...

This problem was found in my gre test practice guide and i am having trouble understanding why the answer i chose was wrong. x^2 =16 y^3= 64 Which is bigger x or y? I chose that they were both equal to 4 however the answer stated that the relationship cannot be determined from the...

The book and lecture notes do not give a good example of how to solve this type of problem. After writing out f' I don't know how to simplify. Any hints? \begin{array}{l} f(x) = x - 5(x - 1)^{2/5} \\ \\ f'(x) = \frac{{f(x + h) - f(x)}}{h} = \frac{{(x + h) - 5((x + h) - 1)^{2/5} -...

Dear all, Does anyone know how to determine which of the following sum is larger? Thanks a lot! \sum_{i=1}^n a_i^{1/3}\sum_{i=1}^n a_i n\sum_{i=1}^n a_i^{4/3} a_i>0 \forall i This is two polynomial of the same order. It is not clear to determine which one is larger, if I...

Hi dudes, don't be put off by the clumsy notation here. I was wondering about these particular exponent towers and this curious property of theirs... Let p be a positive integer. Then the exponent tower, composed of p+1 parts each of value p^(1/p), equals p. e.g. for p=2. tower part...

How do you do this problem (without a calculator) that looks deceivingly simple, yet is utterly confusing. (2 ^ 30 - 2 ^ 29)/2 = ?. The answer is 2 ^ 28, but how was this done without using a calculator. The furthest I can take this without using a calculator is 2 ^ 29 - 2 ^ 28

1 = a^{b} How can I isolate b in that equation? Thanks. ^^

\sqrt x = x^ {.5} and \sqrt [.5] x = x^2 They are the same but i want to know why.

i solved ODE with Lagrange method and got stuck with integral \int x^2 e^{\frac{1}{2}x^2+x} dx i couldn't solve it with any method but combined and got the answer that it is \int x^2 e^{\frac{1}{2}x^2+x} dx=C+(x-1)e^{\frac{1}{2}x^2+x} the problem is that i want to do it with proper...

I know there's a formula somewhere, but how do you factor an equation with an exponent of three. In my solution's manual it says: x^3 - x^2 + 11x - 6 = (x-1)(x-2)(x-3) And I'm just trying to figure out how they got that. Thank you.

Infinite Exponent "towers" Please help me solve this problem; I don't even know how to start... Solve for x: x^{x^{x^{x^{...}}}}=2

how to convert an exponent to binary number?