quiz2_solution - MATH235 Calculus 1 Quiz 2 Show all work to...

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MATH235 Calculus 1 Quiz 2 Show all work to receive full credit. Carefully write down your thought process. Your solution must not contain any logical errors. Good luck! 1. Find the slope of the line tangent to the curve f ( x )= x 2 2 x 3atthepoint(2 , 3) by using the limit de±nition of the instantaneous rate of change. Then ±nd the equation of this tangent line. We will calculate the limit lim h 0 f ( x + h ) f ( x ) h to get the general formula for the slope of the tangent line for f ( x x 2 2 x 3. Then, we will plug in x =2toth i s formula to get the slope of the tangent line at the point (2 , 3). lim h 0 f ( x + h ) f ( x ) h =l im h 0 (( x + h ) 2 2( x + h ) 3) ( x 2 2 x 3) h , h 0 ( x 2 +2 xh + h 2 2 x 2 h 3) ( x 2 2 x 3) h , h 0 x 2 xh + h 2 2 x 2 h 3 x 2 x +3 h , h 0 2 xh + h 2 2 h h , h 0 (2 x + h 2) , =2 x 2 . Therefore, the slop of the tangent line at the point (2 , 3) is 2 × 2 2=2 .
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quiz2_solution - MATH235 Calculus 1 Quiz 2 Show all work to...

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