Calc Limits

posted by .

lim (1+x)^1/x. Give an exact answer.

This reads:
The limits as x approaches zero is (1 plus x) to the 1 divided by x.

The log of each term is
(1/x) ln (1 + x) = ln (1+x)/x
Using L'Hopital's rule for the limit of
f(x)/g(x), the limit if the log is
lim f'/g' = lim [1/(1+x)]= 1
and the antilog of that is e. 2.71828...

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc Help

    Find the derivative. Express answer in radical notation with no negative exponents. s=4(sqroot t)+(3/t)+2t^5 This reads (4 times the square root of t) plus (3 divided by t) plus 2t to the 5th. Differentiate it one term at a time, using …
  2. Calculus-Limits

    Okay, i posted this question yesterday, however, I did not really understand the answer I received. If your the one who answered my question, could you please elaborate. If not, could you try to answer this tough, for me, question. …
  3. Calculus

    We are doing limits in Calculus, but now we are doing trig limits too and i do not get how to do any of them. For example ones like this, how do you do them?
  4. Maths (limits)

    how do i evaluated these limits: lim x --> 3 ((square root of x^2 +16)- 5)/(x^2 - 3x) lim x--> to infinity (2+ 100/x)
  5. math

    i need some serious help with limits in pre-calc. here are a few questions that i really do not understand. 1. Evaluate: lim (3x^3-2x^2+5) x--> -1 2. Evaluate: lim [ln(4x+1) x-->2 3. Evaluate: lim[cos(pi x/3)] x-->2 4. Evaluate: …
  6. Calc. Limits

    Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity?
  7. Maths Calculus Derivatives & Limits

    Using the definition of the derivative evaluate the following limits 1) Lim h---> 0 [ ( 8 + h )^1/3 - 2 ] / h 2) Lim x ---> pi/3 ( 2cosx - 1 ) / ( 3x - pi)
  8. Calculus

    Determine the behavior of limits A. Limit as x approaches 1 of: (log x)/((x-1)^2) B. Limit as x approaches infinity of: ((x-1)^2)/(log x))
  9. Limits

    Lim of [1/(3+x)]-(1/3)/x as x approaches 0 is?
  10. AP Calc (Limits)

    I'm trying to factor this equation in order to find its limit, but I'm not sure how to go about it. I can get the answer by graphing on a calculator but I need to do it without one. Function: F(x)=(x^2-36)/(sqrt(x^2-12x+36)) left, …

More Similar Questions