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Math Help - Homework help please!!!!!!!

  1. #1
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    Homework help please!!!!!!!

    Evaluate the following limits:
    A) lim x^2+10x-39/x-3
    x to 3


    B) Lim x-2/(squareroot of x+2)-2
    x to 2


    C) lim 2x^2-5x+3/5x^2-6
    x to infinity


    Problem 2
    Desribe or sketch an example where a function is continuous but not differentiable. Explain why it is continuous but not differentiable..
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  2. #2
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    Quote Originally Posted by vc15ao4 View Post
    Evaluate the following limits:
    A) lim x^2+10x-39/x-3
    x to 3
    Factor,
    x^2+10x-39=(x-3)(x+13)

    B) Lim x-2/(squareroot of x+2)-2
    x to 2
    x - 2 = (x+2) - 4
    Difference of two squares,
    [sqrt(x+2) - 2 ]*[sqrt(x+2) + 2]
    Now cancel numerator and denominator.

    C) lim 2x^2-5x+3/5x^2-6
    x to infinity
    Divide numerator and denominator by x^2

    (2 - 5/x + 3/x^2)/ (5 - 6/x^2)

    As x---> BIG

    We have,

    (2-0+0)/(5-0)
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  3. #3
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    Quote Originally Posted by vc15ao4 View Post
    Problem 2
    Desribe or sketch an example where a function is continuous but not differentiable. Explain why it is continuous but not differentiable..
    Consider the function f(x) = |x|.

    This function is continous because |x| = sqrt(x^2) and both x^2 and sqrt(x) are continous so if there composition.

    But it is not differenciable.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    Evaluate the following limits:
    A) lim x^2+10x-39/x-3
    x to 3


    B) Lim x-2/(squareroot of x+2)-2
    x to 2


    C) lim 2x^2-5x+3/5x^2-6
    x to infinity
    Here

    EDIT: you're too quick for me TPH! I was going to use that example for the second problem as well
    I approached B) a different way, but your way seems nicer
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