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    Simplifying Limits and DNE's

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    1. Evaluate the following limits.

    a) lim 2x^2 + 0x - 18/x^3 - 27=______.
    x->3

    b) lim (9x + 6)^-1 - 24^-1/x - 2=_______.
    x->2

    2. Let f(x)= {x^2 + 1, x<-4
    {-3x + 2, -4<x<5
    { 2/x, 5<x

    a) lim f(x)=________.
    x->-4^-

    b) lim f(x)=________.
    x->-4^+

    c) lim f(x)=_________.
    x->5^-

    d) limf(x)=_________.
    x->5^+

    3. Find the following limits. If needed, enter DNE for all limits that are undefined or do not exist.

    a) Consider the function f(x)= (x - 1)^3/(x + 1)^3 (x - 4)^3

    lim f(x)=_______.
    x->-1^+

    lim f(x)=_______.
    x->-1^-

    lim f(x)=_______.
    x->1+

    lim f(x)=_______.
    x->1-

    lim f(x)=_______.
    x->4^+

    lim f(x)=_______.
    x->4^-

    b) Consider the function g(x)= (x - 7)^2 (x-1)^3/ sqrt(x-5).

    lim g(x)=______.
    x->7^+

    lim g(x)=______.
    x->7^-

    lim g(x)=______.
    x->5^+

    lim g(x)=_______.
    x->5^-

    lim g(x)=_______.
    x->1^+

    lim g(x)=_______.
    x->1^-

    4. Evaluate the following limits.

    a) lim -5x^4 + 2x^2 + 11/ 7x^2 + 10 =________.
    x->infinity

    lim -5x^4 + 2x^2 + 11/ 7x^2 + 10 =________.
    x->-infinity

    b) lim 10x^3 + 3/ -4x^4 + 6x^3 + 15 =_________.
    x->infinity

    lim 10x^3 + 3/ -4x^4 + 6x^3 + 15 =_________.
    x->-infinity

    c) lim 3x^4 - 1x^3 + 9/10x^4 - 9x^2 + 2 =________.
    x->infinity

    lim 3x^4 - 1x^3 + 9/10x^4 - 9x^2 + 2 =________.
    x->-infinity

    5. Evaluate the following limits. Enter DNE for does not exist.

    a) lim (sqrt(x^2 - 5x + 1) - x)=_________.
    x->infinity

    b) lim (sqrt(x^2 - 5x + 1) - x)=_________.
    x->-infinity.

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    https://brainmass.com/math/basic-calculus/simplifying-limits-dnes-296541

    Solution Summary

    The solution assists with simplifying limits and DNE's.

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