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Math Help - Find the tangent line

  1. #1
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    Find the tangent line

    check my answers plz

    1. y = xe^x - 1 at x = 0

    My solution:

    f^1(x) = e^x+ xe^x
    f^1(0) = e^0+ 0e^0
    =1

    Therefore,

    y-(-1) = 1(x-0)
    y = x - 1

    2. y = x Inx at x = 1

    My solution:

    f^1(x) = x(1/x) + Inx
    = In x
    f^1(1) = In 1
    = 0

    Therefore,

    y-0 = 0(x-1)
    y= 0


    Addition question... how can I use math symbols in the forum... I mean the real symbols not like ^ sqrt these kind thing
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  2. #2
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    Your first one is fine, but:

    Quote Originally Posted by jkami View Post
    2. y = x Inx at x = 1

    My solution:

    f^1(x) = x(1/x) + Inx
    = In x
    f^1(1) = In 1
    = 0
    f'(x) = x\left(\frac1x\right)+\ln x=\frac xx+\ln x=1+\ln x,\,x>0

    So f'(1) = 1 + \ln1 = 1\text.
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