CK-12-Calculus

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org P( 10 ≤x≤ 10. 5 ) = ∫ 10. 5 10 1 ( 0. 1 )√ 2 πe ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals f( 9 ) =( 0. 1 )^1 √ 2 πe−(^9 −^10.^2 )^2 /(^2 (^0.^1 )^2 )dx ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org That is, P( 85 ≤x≤ 115 )≈68%. Which says that 68 ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals and Just Math Tutoring, Work and Hooke’s Law, Example 2 (6:52) ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org Review Questions A particle moves along thex−ax ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Supposef(x)is the probability density function for the lifeti ...

http://www.ck12.org CHAPTER 6 Transcendental Functions Chapter Outline 6.1 Inverse Functions 6.2 EXPONENTIAL ANDLOGARITHMICFUNCT ...

http://www.ck12.org Chapter 6. Transcendental Functions 6.1 Inverse Functions Functions such as logarithms, exponential function ...

6.1. Inverse Functions http://www.ck12.org Example 1: Determine whether the functions are one-to-one: (a)f(x) =|x|(b)h(x) =x^1 / ...

http://www.ck12.org Chapter 6. Transcendental Functions The Inverse of a Function We discussed above the condition for a one-to- ...

6.1. Inverse Functions http://www.ck12.org How to find the inverse of a one-to-one function: To find the inverse of a one-to-one ...

http://www.ck12.org Chapter 6. Transcendental Functions It is important to note that for the functionf(x) =x^2 to have an invers ...

6.1. Inverse Functions http://www.ck12.org Solution: Sincef′(x) = 15 x^4 + 2 >0 for allx∈R,f−^1 (x)is differentiable at all v ...

http://www.ck12.org Chapter 6. Transcendental Functions f(x) =x− 31 In problems #4 - 6, use the horizontal line test to verify ...

6.3 Differentiation and Integration of Logarithmic and Exponential Functions 6.2 Exponential and Logarithmic Functions Learning ...

http://www.ck12.org Chapter 6. Transcendental Functions This is equivalent to the exponential form by=x. For example, the follow ...

6.2. Exponential and Logarithmic Functions http://www.ck12.org logbx=logbby =ylogbb =y( 1 ) =y. Thusy=f−^1 (x) =logbxis the inve ...

http://www.ck12.org Chapter 6. Transcendental Functions Before we move to the calculus of exponential and logarithmic functions, ...

6.3. Differentiation and Integration of Logarithmic and Exponential Functions http://www.ck12.org 6.3 Differentiation and Integr ...

http://www.ck12.org Chapter 6. Transcendental Functions d dx[logbx] =wlim→x logbw−logbx w−x =wlim→xlogwb−(wx/x) =wlim→x [ 1 w−xl ...