Cal

10. For f(x)=lnx, construct tables, rounded to four decimals, near x=1, x=2, x=5, and x=10. Use tables to estimate f'(1), f'(2), f'(5) and f'(10). Then guess a general formula for f'(x).
I don't understand how to do number 11

11. Estimate f'(2) using the values of f in the table.

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  1. ln (1) = 0
    ln(1.1) = .09531
    dy/dx = .09531/.1 = .9531

    ln 2 = .69315
    ln 2.1 = .74194
    dy/dx = .04879/.1 = .4879

    ln 5 = etc

    ln 10 = 2.30258
    ln 10.1 = 2.31253
    dy/dx = 0.09950 which is about 1/10

    looks like 1/x in the end

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