Download presentation

Presentation is loading. Please wait.

Published bySierra Trujillo Modified over 3 years ago

1
An Introduction to Calculus

2
Calculus Study of how things change Allows us to model real-life situations very accurately

3
Topics (not in order) Limits Slope of a curve Tangent Lines Extreme values of a curve Area under a curve/volume of a region Lengths Riemann Sums (Finite & Infinite) Rates of Change

4
Before Calculus After Calculus Find slope of a line Calculate average speed of a car Calculate area/volume of rigid geometric figures Find slope of a curve at a point Determine exact speed of a car at a particular time Determine area/volume of any figure under any curve/region

5
Two Main Problems to Solve: I. Tangent Line Problem: How do you find the equation of the tangent line to the graph of a curve at a particular point? II. Area Under Curve Problem: How can you find the area underneath a curve and above the x-axis?

6
f(c) f(c+ x c c+ x Secant line Tangent line Secant line c+ x f(c+ x

7
As x decreases ( x0), secant line approaches the tangent line.

8
abx1x1 x2x2 x3x3 x x x x

9
abx1x1 x2x2 x3x3 x x x x x x x x x4x4 x5x5 x6x6 x7x7

10
As the number of rectangles increases, the sum of their areas approaches the exact area of the curve.

Similar presentations

OK

Maximal Independent Subsets of Linear Spaces. Whats a linear space? Given a set of points V a set of lines where a line is a k-set of points each pair.

Maximal Independent Subsets of Linear Spaces. Whats a linear space? Given a set of points V a set of lines where a line is a k-set of points each pair.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on water scarcity facts Ppt on personality development for mba students Opening ppt on mac Ppt on happy teachers day Ppt on mauryan dynasty Ppt on steve jobs download Ppt on railway track construction Ppt on urinary tract infection in children Mp ppt online Ppt on earthquakes and volcanoes