CK-12-Calculus

1.6. Evaluating Limits http://www.ck12.org Lesson Summary We learned to find the limit of basic functions. We learned to find t ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity MEDIA Click image to the left for use the URL below. URL: http: ...

1.7. Continuity http://www.ck12.org 1.7 Continuity Learning Objectives A student will be able to: Learn to examine continuity o ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity The seeming contradiction is due to the fact that our original ...

1.7. Continuity http://www.ck12.org Definition: The functionf(x)iscontinuous atx=aif the following conditions all hold: 1.ais in ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity Since the domain off(x) =√xisx≥0, we see that that limx→ 0 √xdo ...

1.7. Continuity http://www.ck12.org We see that limx→ 0 +|xx|=1 and also that limx→ 0 −|xx|=−1. Properties of Continuous Functio ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity We will conclude this lesson with a theorem that will enable us ...

1.7. Continuity http://www.ck12.org Of course we could zoom in on the graph to see that the lowest point on the graph lies withi ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity Multimedia Links For a presentation of continuity using limits( ...

1.7. Continuity http://www.ck12.org Prove the Intermediate Value Theorem: If a function is continuous on a closed interval[a,b] ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity 1.8 Infinite Limits Learning Objectives A student will be able ...

1.8. Infinite Limits http://www.ck12.org Atx=1, we have the situation where the graph grows without bound in both a positive and ...

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity Since our original function was roughly of the form f(x) =^1 x, ...

1.8. Infinite Limits http://www.ck12.org limx→∞(x(−x+ 2 )^22 )−^21 limx→ 1 +(x(−x+ 2 )^22 )−^21 limx→∞^2 xx+− 11 limx→−∞ ...

http://www.ck12.org Chapter 2. Derivatives CHAPTER 2 Derivatives Chapter Outline 2.1 Tangent Lines and Rates of Change 2.2 THEDE ...

2.1. Tangent Lines and Rates of Change http://www.ck12.org 2.1 Tangent Lines and Rates of Change Learning Objectives A student w ...

http://www.ck12.org Chapter 2. Derivatives y−y 0 =mtan(x−x 0 ). Example 1: Find the slope of the tangent line to the curvef(x) = ...

2.1. Tangent Lines and Rates of Change http://www.ck12.org Example 2: Iff(x) =x^2 − 3 ,findf(x)and use the result to find the sl ...

http://www.ck12.org Chapter 2. Derivatives y′=limh→ 0 ( 1 x+h )− 1 x h =limh→ 0 xx−(xx+−hh) h =limh→ 0 hxx−(xx+−hh) =limh→ 0 hx( ...