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# Tangent and the Derivative.docx

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School
University of Alberta
Department
Mathematics
Course
MATH100
Professor
Ian Blokland
Semester
Winter

Description
Tangent and the Derivative at a point text 312dt49tFalling object How fast is the object going at t1dd2d1vaverageSlope of secant line tt2t1Actual speed at tis the slope of the tangent line1 d2d1vt1limt2t1t2t1t2t1hLet t2t1meansh0Then 22dt1hdt149t1h49t1vt1limlimSo hhh0h0Figuredt49t2222t12t1hht149lim49lim2t1h492t198t1hh0h0Now lets do the same thing for other functions fxWe want to find the slope of the tangent line of fx at xx0fxhfx00mlimSlope hh0xx0We call this slope the derivative of fx at 1fxExample Find the slope of this function at xax
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