first question:
could x^5-1 simplified?

what is the limit of cuberoot(x^2-5x-4) as x approaches 4?

For the first one:
could x^5-1 simplified?
Yes, the expression can be factored as the 5th roots of unity. First, divide it by (x-1) to get (x^5-1)=(x-1)*4th deg poly. I'm not going to do the work, so you'll have to do the division. The 4th degree poly can be factored furthered , but I doubt you'd be expected to know how to do this in high school algebra.

For the second question:
what is the limit of cuberoot(x^2-5x-4) as x approaches 4?

We want the lim x->4 of x^2-5x-4
This is the same as (lim x->4)^2 -5(lim x->4) -4 =
16-20-4 = -8
We can take the limit inside of continuous functions, and all polys are continuous. This should be proven as a theorem in your text somewhere. Sometimes it's in the appendix for an intro text.

For the 2nd one I see I missed the cube root part. The limit can still be taken inside, but you'll need to take the 3rd root of the expression. Thus we have,
((lim x->4)^2 -5(lim x->4) -4 =
16-20-4)^(1/3) = something you can do.

BTW, you should read the expression "lim x->4" as the limit of x as x approaches or tends to 4.

Just to reiterate too, if f(x) is continuous, then the lim x->a of f(x) = f(lim x->a). There should be a statement or result to the effect that polynomials of all degrees are continuous, therefore we can evaluate the limit for x=a. If the function is not continuous at a point 'a' we need to look at left and right hand (or one-sided) limits.

i didn't really understand what you meant by 4th deg poly, or what exactly i have to do.

do i just do synthetic division, (x^5-1)/(x-1)?

Yes. I had forgotten what the expression for this was, I see what I meant was synthetic division. I'm more accustomed to the word 'factor(ing)' to describe this process.
In general, if a poly of degree n is factored as two polys of deg p and q, then n=p+q. The degree of a poly is the degree of it's highest term. In this case, x^5-1 should factor as
(x-1)(x^4 + lower degree terms) I don't know if you're exected to factor the x^4 poly, but it does factor; it requires result about the roots of unity to do it.

  1. 👍 0
  2. 👎 0
  3. 👁 221

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x? a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity b. f(x) approaches negative

  2. calculus

    A state charges polluters an annual fee of $20 per ton for each ton of pollutant emitted into the atmosphere, up to a maximum of 4,000 tons. No fees are charged for emissions beyond the 4,000-ton limit. Write a piecewise de nition

  3. Math (Limits)

    What is the limit of g(x)=x as x approaches pi? Would it just be pi??

  4. Social studies

    Which of the following drives the free market economy? ○A. the needs and wants if people ○B. the supply of goods in the market ○C. the number of consumers in the market ○D. The gross domestic product I don't understand

  1. Calculus

    Find the limit lim as x approaches (pi/2) e^(tanx) I have the answer to be zero: t = tanx lim as t approaches negative infi e^t = 0 Why is tan (pi/2) approaching negative infinity is my question?

  2. Calculus

    Let f be a function defined for all real numbers. Which of the following statements must be true about f? Which might be true? Which must be false? Justify your answers. (a) lim of f(x) as x approaches a = f(a) (b) If the lim of

  3. Calculus Limits

    Question: If lim(f(x)/x)=-5 as x approaches 0, then lim(x^2(f(-1/x^2))) as x approaches infinity is equal to (a) 5 (b) -5 (c) -infinity (d) 1/5 (e) none of these The answer key says (a) 5. So this is what I know: Since

  4. calculus

    find the limit of f'(x) = 1/(√x) using the limit definition of derivative as x approaches 0.

  1. Math

    How do I find the limit as x approaches 4 from the right when f(x)= (4-x)/l4-xl ?

  2. Calculus

    Find limit as x approaches 5 (x^2-3x-10)/(x-5)

  3. Calculus

    1. Evaluate the function at the given numbers (correct to six decimals places). Use the results to guess the value of the limit,or explain why it does not exist. F(t)=( t^(1/3) - 1)/(t^(1/2) - 1) ; t= 1.5,1.2,1.1,1.01,1.001; The

  4. Algebraic limits

    The limit as x approaches infinity. (1)/(5^x) The limit as x approaches 1. (1-x^3)/(2-sqrt(x^2-3)) Show your work thanks in advance!

You can view more similar questions or ask a new question.