Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

Evaluate the limit. if the limit does not exist explain why. a) lim[x:(-2),(x^3+8)/(x+2)]?

b) lim[x:5,(x-5)/|x-5|]

c)lim[x:8,1/(x-8)]

it would help a lot if you guy can show the work so i can learn how to do it! thank

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  • 7 years ago
    Favorite Answer

    for problems of the type 0/0 or inf/inf, one uses a concept call L'Hopital's rule in order to simplify the equation. Look it up on wikipedia

    a) with x : -2, the equation reduces to the form 0/0. Hence you can use L'Hopital's rule.

    Differentiating numerator and denominator, w.r.t. x

    required limit = lim [x:-2], 3x^2 = 3(-2)^2 = 12

    b) this is again of the form 0/0, so differentiate w.r.t x, which means required limit = 1

    c) this one is of the form 1/0 so you cannot use the rule. The limit in this case is "infinity"

    Source(s): Graduate in Applied Physics
  • 4 years ago

    factor the denominator (x^3+8) utilising sum of ideal cubes and then component to it is going to cancel with the numerator (x+2). Then stick in -2 everywhere you spot an x and notice what it provides. this could be your answer.

  • 7 years ago

    a) = lim ( x -- > - 2 ) 3x^2

    = 18

    b) DNE

    c) DNE

    Source(s): my brain
  • 7 years ago

    wo

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