1.1 Preview to calculus

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

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

Answer

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

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

Answer - I

Answer - II

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