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9-81.
1. Mathematics is full of all kinds of amazing equations, but it is comforting to know that some things remain constant for all of them. For example, to find the slope of the tangent line of a function at x = 2, you can follow the same procedure, regardless of the function. For each of the following functions, first find the formula for the slope of a secant line for the function from 2 to 2 + h, then let h → 0 to find the slope of the tangent line at x = 2. Use your calculator to estimate the slopes to three decimal places. Enter a small value for h (such as h = 0.001) in the slope formula to approximate your answer. Homework Help ✎

1. f(x) = 2x2

2. f(x) = 3x

3. f(x) = log x

4. f(x) = cos x (x in radians)

$m=\frac{2(2+h)^{2}-f(2)}{h}$

$m=\frac{\log (2+h)-\log(2)}{h}$

$m=\frac{3^{(2+h)}-3^{2}}{h}$

$m=\frac{\cos(2+h)-\cos(2)}{h}$

Use the eTool below for your estimates.
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