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Unformatted text preview: MATH1010: Chapter 2 cont 1 LIMITS AND DERIVATIVES cont Tangents, Velocities, and Other Rates of Change (2.7, pg. 149) Recall: We introduced the limit concept to find slopes of tangent lines. Now that we have techniques for computing limits, lets return to this original task. To view an animation of this in Maple, type: > with(Student[Calculus1]): TangentSecantTutor(); Definition: The tangent line to the curve ) ( x f y = at the point )) ( , ( a f a P is the line through P with the slope a x a f x f m a x = ) ( ) ( lim provided that the limit exists. Application: If the position of a particle is given by 2 ) ( t t s = , find the instantaneous velocity at 1 = t , where t is time measured in seconds. MATH1010: Chapter 2 cont 2 We can also introduce an alternative expression for the slope of the tangent, where we consider point Q to be a distance h away from P often, this definition is easier to work with....
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