limit of (|x+h|-|x|)/h as h goes to 0 at x=4

why is the answer 1?

  1. 👍
  2. 👎
  3. 👁
  1. observe that we can further simplify (|x+h|-|x|)/h to
    (x + h - x)/h
    lim 1 as h->0 at x = 4 is equal to 1, since the limit of a constant is also equal to that constant.

    hope this helps~ :)

    1. 👍
    2. 👎
  2. thank you, i got it

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Use this definition with the right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. f(x)= 3+sin^2(x) 0

  2. 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

  3. Calculus

    The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim n → ∞ [f(x1)Δx + f(x2)Δx + . . . + f(xn)Δx] Use this definition to

  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? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if

  1. limits

    what is the derivative of e^(3*ln(x^2)) i keep getting 6/x * e^(3*ln(x^2)) but that's not one of the multiple choice so am i doing something wront. also, what is the limit of (1-cosx)/(2*(sinx)^2) as x approaches zero. is the

  2. Math

    Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim t → −1 (t2 + 1)^4(t + 3)^5

  3. math

    evaluate the limit as x approaches 0 from the right. of the function xcos(1/x) I know the answer is O but I am not sure as of my reasoning. I just that that since cos(1/x) is being multiplied by a number approching 0 that the

  4. Calculus

    Consider the function below. f(x) = [1-(4/x)]^x (a) Use a graph to estimate the value of the limit of f(x) as x approaches infinity. (Round the answer to two decimal places.) (b) Use a table of values of f(x) to estimate the

  1. math help

    Find the 95% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers

  2. Calculus. Limits. Check my answers, please! :)

    4. lim (tanx)= x->pi/3 -(sqrt3) 1 (sqrt3) ***-1 The limit does not exist. 5. lim |x|= x->-2 -2 ***2 0 -1 The limit does not exist. 6. lim [[x]]= x->9/2 (Remember that [[x]] represents the greatest integer function of x.) 4 5

  3. Calculus

    Find the limit Limit as h approaches 0 of : SqRt(4+h)-2 ____________ h by relating it to the derivative. (Indicate reasoning.)

  4. math

    Let f(x) = 0 if x < 4 5 if -4 ≤ x < -1 -4 if -1 ≤ x < 5 0 if x ≥ 5 g(x) = ∫ [upper limit x, lower limit -4] f(t)dt Determine g(-5), g(−3), g(0), and g(6). Also, the absolute maximum of g(x) occurs when x = ? and and is

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