Calculus

Find one sided limit

lim x->2+ 1/(1+e^(1/x-2))

  1. 👍 0
  2. 👎 0
  3. 👁 187
  1. Missing Parentheses:
    1/(1+e^(1/x-2)) should read: 1/(1+e^(1/(x-2)))

    Lines below are not rigorous, but demonstrate what happens.

    For x->2+
    1/(1+e^(1/(x-2)))
    =1/(1+e^(1/0+)))
    =1/(1+e^∞)
    =0

    For x->2-
    1/(1+e^(1/(x-2)))
    =1/(1+e^(1/(0-)))
    =1/(1+e^(-∞))
    =1/(1+0)
    =1

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. calc urgent

    Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match. First we find the left limit. lim x→6− f(x)

  3. Calculus, please check my answers!

    1. Evaluate: lim x->infinity(x^4-7x+9)/(4+5x+x^3) 0 1/4 1 4 ***The limit does not exist. 2. Evaluate: lim x->infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 ***2/3 The limit does not exist. 3. lim x->0 (x^3-7x+9)/(4^x+x^3) 0 1/4 1 ***9 The

  4. Calculus

    Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x->0 (1+x)^(1/x) or e= lim as x->infinity (1+1/n)^n Am i able to substitute in x/n for x? and then say that e lim x ->0

  1. 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

  2. Calculus

    Find the positive integers k for which lim ->0 sin(sin(x))/x^k exists, and then find the value the limit. (hint:consider first k=0, then k=1. Find the limit in these simple cases. Next take k=2 and finally consder k>2 and find the

  3. 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

  4. 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

  1. calculus again

    Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily that a. g is not defined at x=0 b. the limit of g(x) as x approaches equals 1 c.g is not continuous at x=0 d.g'(0) = 1 The answer is d, can someone please explain how?

  2. calc

    need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting the limit for the numerator and denominator lim lim x->0 4(e^2x-1) (4)x->0 (e^2x-1) ______________ = ________________ lim lim x->0 e^X-1 x->0 e^x-1 Next solve for

  3. survey of clac

    g(x)={x+6, for x or equal to -2, find the limit: lim g(x)= lim g(x)= x-->-2^- x-->-2^+ lim g(x)= lim g(x)= x-->-2^+ x-->4^-

  4. Limits

    Is there any theorem like, that the limit of the average value of an infinite series takes the same value as the original sequence? Let lim n->infinity (an) = a be given(i.e. converges) Then the sequence bn is defined as follows,

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