1.1 Preview to calculus

1. 1.1 Preview to calculus

2. Tangent line problem • Goal: find slope of tangent line at P • Can approximate using secant line • First, let • Second, find slope of secant line between P and Q • Note that as Q approaches P (really close Q x-values), slope of secant line approaches slope of tangent line so… slope of tangent line = limit of slope of secant line

3. Estimating slope of tangent line at P • Find the slope of each secant line. Estimate the slope of tangent line at P. Given points that line on

4. Answer

5. Area problem • Goal: find area of a plane region bounded by graphs of functions • First, divide area into rectangles of = width (either below or above the top function) • As increase # of rectangles, approximation gets better because less area is missed by rectangles

6. Determining approximate area under curve • Approximate area under between x=0 and x=1using circumscribed rectangles of 2 different widths.

7. Answer - I

8. Answer - II

9. Answer - III • As the # of rectangles increased, the area became more accurate in its approximation. The true area under the curve is 1/3.