math

posted by .

the limit of cuberoot((-3x^3+5x+2)/(x^2-1)) as x approaches 3 is the problem.

how could (-3x^3+5x+2) so it would be factored out with denominator?

thanks!


If you read the answer I gave for the previous question, then you can take the limit inside to get

lim x->3 of((-3x^3+5x+2)/(x^2-1))^(1/3) becomes
(lim x->3(-3x^3+5x+2)/lim x->3(x^2-1))^(1/3) becomes
(-3(lim x->3)^3+5(lim x->3)+2)/((lim x->3)^2-1))^(1/3) =
(-81+15+2)/(9-1) = something you can do.
Be sure to check my arithmetic.

As for factoring it, you should see that the only factors of the denominator are (x-1) and (x+1). If neither of these divide the numerator, then no further simplifying can be done. (I think one of them should divide it by inspection, but I'll leave the work to you. Write back if you need help or want work checked.)


this one has to be cubed too, is that right?


No, I think I read this one correctly. You have, "the limit of cuberoot[epression]..."
So we will take the limit inside the function, evaluate it, then take the cube-root. The only difference here is that we have the 3rd root of a rational function -a function that is the ratio of two polynomials. Other than that, we can still take the limit inside of each function and evaluate them separately, then take roots.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    first question: could x^5-1 simplified? what is the limit of cuberoot(x^2-5x-4) as x approaches 4?
  2. 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 ?
  3. math

    thanks for the explanation of limit, but i want someone to help check out this problem for me lim x->3 (x^2 - x - 12)/ (x - 3) i got 5 as the answer okay, so i cant use substitution. i factor the (x^2 - x - 12) and got (x - 4) and …
  4. algebra

    1)Simplify:(6x^3-16x^2+11x-5)/(3x-2) answer= 2x^2-4x+1-3over3x-2 2)Factor 27x^3-1 completley. answer= (3x-1)^3 if this isnt correct,im not sure how to solve it b/c this makes the most sense to me. 3)Simplify: x^2-3x-28 over x^2-9x+14,assume …
  5. Calculus

    1. Use the Taylor series to calculate the limit. Problem: limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x). I did the problem out but I need help in seeing if its correct. limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x)= …
  6. 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 …
  7. Math-Calculus

    Hi, I am trying to figure out what the limit as h approaches 0 of (1-2h)^(1/h) is. I am unfamiliar with the process I am supposed to use to solve this limit. I have just been reasoning out this limit, but I keep getting the answer, …
  8. Calculus

    Find the limit as x approaches 1 5/(x-1)^2 I don't understand how to solve it because there would be a 0 on the denominator.
  9. General Calculus Question

    How do you solve a limit when it approaches infinity and there is a square root in the denominator?
  10. Calc 1 limits

    The equation is x^2+6x+9/x^4-81 Limit is x➡️-3 I factored it out and I got 1/36 would that be right The numerator would factor out to be (x+3)(x+3) then the denominator would be (x+3)(x-3)(x+3)(x-3) this would cancel …

More Similar Questions