CK-12-Calculus

3.7. Optimization http://www.ck12.org We first note that since this is a real-life application, we observe that both quantities, ...

http://www.ck12.org Chapter 3. Applications of Derivatives We started with the general volume formulaV=^13 πr^2 h, but quickly r ...

3.7. Optimization http://www.ck12.org The feasible domain of this function is 0<×< 45 ,which makes sense because ifxis 45 ...

http://www.ck12.org Chapter 3. Applications of Derivatives dAdr = 4 πr− (^946) r 2 =0 whenr=^3 √ 946 4 π ≈^9 .06 cm. We note tha ...

3.7. Optimization http://www.ck12.org Review Questions In problems #1–4, find the absolute maximum and absolute minimum values, ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.8 Approximation Errors Learning Objectives A student will be able t ...

3.8. Approximation Errors http://www.ck12.org The linear approximation can be used to approximate functional values that deviate ...

http://www.ck12.org Chapter 3. Applications of Derivatives the differences between the actual and approximate values, we can ent ...

3.8. Approximation Errors http://www.ck12.org Tn(x) =f(a)+f′(a)(x−a)+f ′′(a) 2! (x−a) (^2) +...+fn(a) n! (x−a) n. We call this t ...

http://www.ck12.org Chapter 3. Applications of Derivatives We get a slightly better approximation for the quadratic than for the ...

http://www.ck12.org CHAPTER 4 Integration Chapter Outline 4.1 Indefinite Integrals Calculus 4.2 THEINITIALVALUEPROBLEM 4.3 THEAR ...

http://www.ck12.org Chapter 4. Integration 4.1 Indefinite Integrals Calculus Learning Objectives A student will be able to: Fin ...

4.1. Indefinite Integrals Calculus http://www.ck12.org With our definition and initial example, we now look to formalize the def ...

http://www.ck12.org Chapter 4. Integration ∫ exdx=ex+C. Again we could easily prove this result by differentiating the right sid ...

4.1. Indefinite Integrals Calculus http://www.ck12.org ∫ e^3 xdx=e 3 x 3 +C. We can now re-state the rule in a more general form ...

http://www.ck12.org Chapter 4. Integration Review Questions In problems #1–3, find an antiderivative of the function f(x) = 1 − ...

4.2. The Initial Value Problem http://www.ck12.org 4.2 The Initial Value Problem Learning Objectives Find general solutions of ...

http://www.ck12.org Chapter 4. Integration Solution: We can re-state the problem in terms of a differential equation that satisf ...

4.2. The Initial Value Problem http://www.ck12.org f′(x) = 3 x^2 +e^2 xandf( 0 ) = 3. f′(x) =^3 √ x^2 −x^12 andf( 1 ) = 3 f′( ...

http://www.ck12.org Chapter 4. Integration 4.3 The Area Problem Learning Objectives Use sigma notation to evaluate sums of rect ...