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Math Help - Continuity (ii)

  1. #1
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    Continuity (ii)

    f(x) = { [(e^x) - 1] / x ; if x not equal 0
    ...... .{ b ...................; if x = 0

    What value of b makes f continuous at x = 0?

    so.. the left side and right side must be equal in order to make
    f continuous at x = 0

    [(e^x) - 1] / x = b
    [(e^x) - 1] = (b)(x)
    e^x = (b)(x) + 1
    .
    .
    .
    dont know how to proceed..

    should i introduce ln?
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  2. #2
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    Quote Originally Posted by nameck View Post
    f(x) = { [(e^x) - 1] / x ; if x not equal 0
    ...... .{ b ...................; if x = 0

    What value of b makes f continuous at x = 0?

    so.. the left side and right side must be equal in order to make
    f continuous at x = 0
    No, \frac{e^x-1}{x} is not defined at x= 0. It is the limit of that that must be equal to b in order that the function be continuous.
    Take the limit, perhaps using L'Hopital's rule, to find b.

    [(e^x) - 1] / x = b
    [(e^x) - 1] = (b)(x)
    e^x = (b)(x) + 1
    .
    .
    .
    dont know how to proceed..

    should i introduce ln?
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  3. #3
    Member
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    151
    got it!!
    b = 1
    correct?
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