Limit definition Definition and 58 Threads

Is it possible to evaluate the limit definition of e: lim (1+1/n)^n ? n->INF I have seen approximations using binomial theorem, but I am curious as to if the limit could be rearranged and evaluated using L'hopital for instance. thanks

Homework Statement I want to solve for the derivative of e^x using the limit definition. Homework Equations http://www.math.hmc.edu/calculus/tutorials/limit_definition/img10.png The Attempt at a Solution obviously the derivative of e^x is itself, so i konw the answer. i just...

I have to differentiate some problems using the limit definition (f(x+h)-f(x)\h), but Iam having some trouble on a couple. 1. Square root of 30 is 0 because its a constant correct? 2. R(t) = 5t^(-3/5) <---- I have tried this problem many times with the definition, but I can't come up with...

Please any help. Use the symbols \beta and \sigma definition of limit to prove that limit (x,y)\Longrightarrow(0,0)x+y/x\x^2+y\y^2=0

First 3 definitions: \begin{array}{l} \left( 1 \right)\mathop {\lim }\limits_{n \to \infty } P\left( {\left| {X_n - X} \right| > \varepsilon } \right) = 0 \\ \left( 2 \right)P\left( {\mathop {\lim }\limits_{n \to \infty } X_n = X} \right) = 1 \\ \left( 3 \right)\mathop {\lim...

i didnt understand delta definiton anyone can explain?

show by example that the stament for all d>0 there exists e>0 such that o<|x-a|<d -> |f(x）-L|<e is Not the definition of limit. would somebody give me a hint?

Hello guys! I'm new here! Well, it feels like this forum is cool and interesting! Can anyone help me here? =) How do you prove the quotient theorem using the limit definition? (Given a limit of f of x as x approaches a is A and a limit of g of x as x approaces a is B).