limit calc question

posted by .

2 questions!!!

1.

Limit X approaching A

(X^1/3-a^1/3)/ x-a

2.
LiMIT x approaching 0
(1/3+x – 1/3) /x





On the first, would it help to write the denominator (x-a) as the difference of two cubes ((x^1/3 cubed - a^1/3 cubed)

second. use LHopitals rule. Take the derivative of the numerator, derivative of the denominator.

what if u never learned the lhopitals rule

All you have to do is to take the derivative of both numerator and denominator. That's L'Hopital's rule

If you never learned L'Hopital's rule, you should derive it first. Suppose that f(a) = g(a) = 0

Lim x--> a f(x)/g(x) =

Lim h--->0 f(a+h)/g(a+h) =

Lim h--->0
(f(a+h)- f(a))/(g(a+h) - g(a)) =

Lim h--->0
[(f(a+h)- f(a))/h] /(g(a+h) - g(a))/h] =

The limit of a quotient is the quotient of the limits provided both limits exists and the quotient of the limits also exists.

  • limit calc question -

    1. consider the question to look like this

    lim (x^(1/3) - a^(1/3) ) / ( (x^1/3)^3 - (a^1/3)^3) as x ----> a

    =lim (x^1/3 - a^1/3)/[ (x^1/3) - a^1/3)(x^(2/3) +x^1/3 a^1/3 + a^2/3) ] as x--->a
    = lim 1/ (x^1/3) - a^1/3)(x^(2/3) +x^1/3 a^1/3 + a^2/3) as x --> a
    = 1/(a^2/3 + a^1/3 a^1/3 + a^2/3)
    = 1/(3 a^(2/3)

    2. without L'Hopital's rule

    lim (1/(3+x) - 1/3 )/x , as x-->0
    = lim [(3 - 3 - x)/(3(3+x)) / x
    = lim [ -x/(3(3+x))/x
    = lim -1/(3(3+x)) as x-->0
    = -1/9

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc limit

    lim (2^x - 3^-x)/2^x + 3^-x x-> infinity Thanks. Do you mean (2^x - 3^-x)/(2^x + 3^-x) or [(2^x - 3^-x)/2^x] + 3^-x ?
  2. Calculus...

    How can I use the "angle addition formula" and the formula "limit of x approaching 0 of sin(x)" to show that the limit of x approaching 0 sin(a+x) = sin(a) for all a?
  3. Calculus- limits

    f(x) = x + 7 if x < or equal to 5 F(x) = 7 if x >5 what is the limit as x is approaching 5 from the left side?
  4. Calculus

    Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous?
  5. Calculus

    Could someone please help me with these questions;I was having trouble with these four questions. Evaluate each limit, if it exists, using any appropriate technique. 1.) The limit as u approaches 4; u^2-16/u^3-64 2.) The limit as x …
  6. Calculus

    lim x-->0+ f(x), where f(x)= x ln x values for x are 1,0.5,0.1,0.05,0.01,0.005,0.001 when i plugged in 1 i got 0 then -.34657 then -.23025 ................... leading up to -0.00690 what is the value of the limit is it approaching …
  7. AP Calculus AB

    how do you solve limit approaching 0 of (sin^2x) / (x)
  8. Digital Circuits

    which is the primary purpose of a resistor in series with a led being driven by a flip-flop a. Limit voltage b. Limit current c. Limit speed d. Limit power
  9. Calculus

    I am trying to solve a sigma/summation notation problem: n = 99, i = 4 and each term in the sequence is determined by (1/i) - (1/(i+1)). Since n = 99, I think it's safe to assume my professor does not want me to actually go through …
  10. calculus

    I have a definition lim theta approaching 0 sin theta/theta = 1 so show if the limit x approaching 0 sin2x/5=2/5

More Similar Questions