CK-12-Calculus

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 ...

6.3. Differentiation and Integration of Logarithmic and Exponential Functions http://www.ck12.org and in the special case whereb ...

http://www.ck12.org Chapter 6. Transcendental Functions Here we use the Chain Rule: d dx [ln(cos 5x) 3 ]= 1 cos^35 x· [ 3 (cos 5 ...

6.3. Differentiation and Integration of Logarithmic and Exponential Functions http://www.ck12.org ∫ 1 xdx=ln|x|+C. Example 6: Ev ...

http://www.ck12.org Chapter 6. Transcendental Functions Example 8: Evaluate∫tanxdx. Solution: To solve, we rewrite the integrand ...

6.3. Differentiation and Integration of Logarithmic and Exponential Functions http://www.ck12.org d dx[b u] =bu·lnb·du dx. And i ...

http://www.ck12.org Chapter 6. Transcendental Functions f′(x) =√^1 πσ(− 2 αk(x−x 0 ))e−αk(x−x^0 )^2 =−^2 αk√(xπσ−x^0 )e−αk(x−x^0 ...