CK-12-Calculus

7.6. Improper Integrals http://www.ck12.org From the figure above, the area of the region to be revolved is given byA=πy^2 =πx^2 ...

http://www.ck12.org Chapter 7. Integration Techniques So the volume of the solid isπ/ 4. Example 6: Evaluate∫−+∞∞ex+dxe−x. Solut ...

7.6. Improper Integrals http://www.ck12.org ∫+∞ 0 dx ex+e−x=llim→∞ ∫ 1 0 dx ex+e−x =llim→∞[tan−^1 ex]l 0 =llim→∞ [ tan−^1 el−tan ...

http://www.ck12.org Chapter 7. Integration Techniques e.∫ 0 π/^4 tanxdx Evaluate the integral or state that it diverges. 2.∫ 1 ∞ ...

7.7. Ordinary Differential Equations http://www.ck12.org 7.7 Ordinary Differential Equations General and Particular Solutions Di ...

http://www.ck12.org Chapter 7. Integration Techniques Anisocline(for constantk) is the line along which the solution curves have ...

7.7. Ordinary Differential Equations http://www.ck12.org Exercise Sketch the slope field of the differential equationdydx= 1 −y ...

http://www.ck12.org Chapter 7. Integration Techniques Solution. Separatingxandyturns the equation in differential formdyy =xdx. ...

7.7. Ordinary Differential Equations http://www.ck12.org Solution. The solution is given byP= 1 −AeP^00. 05 twhereA=^50001000 −^ ...

http://www.ck12.org Chapter 7. Integration Techniques The Runge-Kutta methods are an important family of implicit and explicit i ...

http://www.ck12.org CHAPTER 8 Infinite Series Chapter Outline 8.1 Sequences 8.2 INFINITESERIES 8.3 SERIESWITHOUTNEGATIVETERMS 8. ...

http://www.ck12.org Chapter 8. Infinite Series 8.1 Sequences Learning Objectives Demonstrate an understanding of sequences and ...

8.1. Sequences http://www.ck12.org The terms of the sequence are: n 1 2 3 4 ... an= n 2 n+ 1 12 1 + 1 = 1 2 22 2 + 1 = 4 3 9 4 1 ...

http://www.ck12.org Chapter 8. Infinite Series To determine the limit, we look at the trend or behavior of the graph of sequence ...

8.1. Sequences http://www.ck12.org The figure above shows the graph of the sequence {ln(n) n } . Notice that fromNon, the terms ...

http://www.ck12.org Chapter 8. Infinite Series Example 7 The sequence{ln(n)}grows without bound asnapproaches infinity. Note tha ...

8.1. Sequences http://www.ck12.org Rules, Sandwich/Squeeze Properties of function limits are also used with limits of sequences. ...

http://www.ck12.org Chapter 8. Infinite Series n→lim+∞ ( 11 n − 8 n^2 ) =n→lim+∞^11 n −nlim→+∞n^82 Applying the rule for the dif ...

8.1. Sequences http://www.ck12.org Thus, limn→+∞ 0 ≤limn→+∞^8 nn!≤limn→+∞(^8 n) ( 87 7! ) . By using the Rules Theorem, we have ...

http://www.ck12.org Chapter 8. Infinite Series Yn(x) =y 0 +∫xx 0 f(t,Yn− 1 (t))dtforn≥ 0 The sequence of approximations converge ...