CK-12-Calculus

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 ...

6.3. Differentiation and Integration of Logarithmic and Exponential Functions http://www.ck12.org MEDIA Click image to the left ...

http://www.ck12.org Chapter 6. Transcendental Functions 6.4 Exponential Growth and Decay Learning Objectives A student will be a ...

6.4. Exponential Growth and Decay http://www.ck12.org So the solution to the equation(dy/dt) =kyhas the formy=Cekt.The box below ...

http://www.ck12.org Chapter 6. Transcendental Functions CancelingCfrom both sides, 1 2 =e kt. Solving fort,which is the half-lif ...

6.4. Exponential Growth and Decay http://www.ck12.org Example 2: A certain population of bacteria increases continuously at a ra ...

http://www.ck12.org Chapter 6. Transcendental Functions t=ln 2k = 0 ln 2. 409 t= 1 .7 hours. This tells us that after about 1.7 ...

6.4. Exponential Growth and Decay http://www.ck12.org A=Pert 30 , 000 = 10 , 000 e(^0.^139 )(t) 3 =e^0.^139 t ln 3= 0. 139 t t= ...

http://www.ck12.org Chapter 6. Transcendental Functions P= 1 + 44994500 e− 0. 8 x = 1 + 44994500 e− 0. 8 ( 7 ) = 1 + 44994500 ( ...

6.4. Exponential Growth and Decay http://www.ck12.org MEDIA Click image to the left for use the URL below. URL: http://www.ck12. ...

http://www.ck12.org Chapter 6. Transcendental Functions Polonium−210 is a radioactive isotope with half-life of 140 days. If a ...

6.5. Derivatives and Integrals Involving Inverse Trigonometric Functions http://www.ck12.org 6.5 Derivatives and Integrals Invol ...

http://www.ck12.org Chapter 6. Transcendental Functions The range is based on limiting the domain of the original function so th ...

6.5. Derivatives and Integrals Involving Inverse Trigonometric Functions http://www.ck12.org d dx [sin− (^1) u]= √ 1 1 −u^2 du d ...

http://www.ck12.org Chapter 6. Transcendental Functions The Integration Formulas of the Inverse Trigonometric Functions The deri ...