Then we will plug in x 9 to this formula to 1 2 get

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Unformatted text preview: . f ( x + h ) − f ( x) We will calculate the limit limh→0 to get the general formula for the h √ slope of the tangent line for f (x) = x. Then, we will plug in x = 9 to this formula to 1 2 get the slope of the tangent line at the point (9, 3). √ √ f ( x + h ) − f ( x) x+h− x lim = lim , h→ 0 h→ 0 h h √ √√ √ ( x + h − x)( x + h + x) √ = lim , √ h→ 0 h ( x + h + x) ( x + h) − x = lim √ √, h→ 0 h ( x + h + x) 1 = lim √ √, h→ 0 x+h+ x 1 = √. 2x 1 1 Therefore, the slop of the tangent line at the point (9, 3) is √ = . 6 29 1 Next, since this tangent line has slope , and it passes the point (9, 3), by the point6 1 1 3 slope formula, the tangent line equation is y − 3 = (x − 9). That is, y = x + 6 6 2...
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This note was uploaded on 02/10/2014 for the course MATH 235 taught by Professor Lucas during the Fall '08 term at James Madison University.

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