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Homework Help: Evaluating Limits

  1. Sep 19, 2007 #1
    I have been given a series of limits to evaluate, where I can only know if I got 100% of them correct or not, as opposed to individually. So, I'm not sure which I have made a mistake on, so I will post all the limits and my work. Thanks

    A)
    lim x/|x|
    x→ 0

    limit does not exist

    B)
    lim [(x^2)-1]/(x-1)
    x→ −1

    =(1-1) / (-1-1) = 0/-2 = 0

    c)
    lim [(x^2)+4x−5]/[(x^2)+x−2]
    x→ 1

    = (x+5)(x-1)/(x+2)(x-1) = (x+5)/(x+2) = 6/3 = 2

    d)
    lim |x|
    x→ 0

    = 0

    e)

    lim [(2t^2)−3t−2]/[(t^2)+t−6]
    t→ 2

    = (2t+1)(t-2) / (t+3)(t-2) = (2t+1)/(t+3) = 5/5 = 1

    f)

    lim[(x^2)−2x+1]/[(x^2)−1]
    x→ 1

    = (x-1)(x-1) / (x-1)(x+1) = (x-1)/(x+1) = 0/2 = 0

    g)
    If f(x)=2x−7 find
    lim (f(x+h)−f(x)) / h
    h→ 0

    =2(x+h)-7 - (2x-7) / h
    = 2x + 2h -7 - 2x + 7 / h
    = 2h / h = 2

    h)
    If f(x)=(2(x^2)+3x+5) find
    lim (f(h)−f(0) )/ h
    h→ 0

    =2(h^2) + 3h +5 -5 / h
    =h(2h+3) / h
    =2h+3 = 3


    i)
    If f(x)=(−25) / (2x+3)
    find

    lim [f(1+h)−f(1)] / h
    h→ 0

    = (25/ 2(1+h) +3) - (25/ 2(1) + 3) /h
    = (25/ 5+2h) - (5) / h
    = (25/ 5+2h) - (5(5+2h))/(5+2h) /h
    = (25-25-10h)/(5+2h) /h
    = -10 / 5+2h
    = -2

    j)
    lim [(x^2)+h] / [x+(h^2)]
    h→ 0

    = (x^2) / x
    = x



    Thanks
     
  2. jcsd
  3. Sep 19, 2007 #2
    For "i" I got 2 -- Other then that looks good
     
  4. Sep 19, 2007 #3

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    I don't see any mistakes except a sign reversal in part i.
     
  5. Sep 19, 2007 #4
    oh, that would be the one
    why is it positive though

    shouldnt it be subracting 25 and 10h?
    i must be missing something

    thanks
     
  6. Sep 19, 2007 #5

    HallsofIvy

    User Avatar
    Science Advisor

    You said the function was f(x)=(−25) / (2x+3)".

    In your calculation, you dropped the "-" from -25 !!
     
  7. Sep 19, 2007 #6
    f(x)=(−25) / (2x+3)

    You solved for

    If f(x)=(25) / (2x+3)
     
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