Find the linearization L(x) of y=e10xln(x) at a=1. L(x) =?

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  • TomV
    Lv 7
    6 months ago

    L(x) = f(a) + [df(a)/dx](x-a)

    Assuming there is an exponent applicable to the "e" term and guessing at what that exponent might be since there are no grouping or exponential symbols provided (Did you proofread your question?)

    y = f(x) = e^(10x)ln(x)

    df/dx = 10e^(10x)ln(x) + e^(10x)/x

    = e^(10x)(10ln(x) + 1/x)

    at x = a = 1

    f(1) = 0

    f'(1) = e^(10)

    L(x) = f(1) + f'(1)(x-1)

    L(x) = e^(10)(x-1)

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