integral

Heating, ventilating, and air conditioning

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Home appliances

Plumbing

Boilers

Water heating

Name:________________________ Date:________________________ AP Calculus BC Class Activity 7b: Integration of Exponential Functions Evaluate the following integrals: 6. Find the average value of the function on the interval [0, 4]. 7. Write an expression and find the area of the region bounded by the curve , the x-axis, and the lines x = ln 3 and x = ln 20. 8. Water is leaking from a broken water heater at a rate in gallons per minute of . Find the total amount of water that leaked from the water heater after 6 minutes. Assume the water heater held twenty gallons at the start. After two minutes of leaking the water heater pulled more in water at a rate of . Find the net change in the amount of water in the heater after 8 minutes.

bccalcclassact7aintsubt

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Velocity

Name:________________________ Date:________________________ AP Calculus BC Class Activity 7a: Integration by Substitution Evaluate the following expressions: 8. Find the area under the curve on the interval . 9. Find the average value of the function on the interval . 10. A particle is moving along the x-axis so that its velocity can be found by the equation Given the starting position (1, 5) find the position of the particle when t = 4 seconds.
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ap calculus

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Differential calculus

rates

derivative

Differentiation rules

Rahn ? 2008 AP Calculus ? Final Review Sheet When you see the words ?. This is what you think of doing 1. Find the zeros of a function. Set the function equal to zero and solve for x. 2. Find equation of the line tangent to f(x) at (a,f(a)). Find f ?(x),the derivative of f(x). Evaluate f ?(a). Use the point and the slope to write the equation: y= f ?(a)(x-a)+f(a) 3. Find equation of the line normal to f(x) at (a,f(a)). Find f ?(x),the derivative of f(x). Evaluate f ?(a). The slope of the normal line is 1 '( )f a ? . Use the point and the slope to write the equation: ( ) ( ) ( ) 1 y x a f a f ? a = ? + 4. Show that f(x) is even. Evaluate f at x = -a and x = a and show they are equal.

2008 AP mc

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Integral calculus

The questions contained in this AP? Calculus BC Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Calculus BC Practice Exam has never been administered as an operational AP Exam, statistical data are not available for calculating potential raw scores or conversions into AP grades. This AP Calculus BC Practice Exam is provided by the College Board for AP Exam preparation. Teachers are permitted to download the materials and make copies to use with their students in a classroom setting

2003 AP MC

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Integration by substitution

Trigonometric functions

Taylor series

Technology

? ? ? ? ? ? ? ? ? ? ? ? ? ? M AREA - COMPLETE THIS AREA AT EVERY EXAMINATION. ~The AP"'ADVANCEDTo maintain lhe security 01 lhe exam and the vaftdily 01 my AP grade, I will allow no one other than myseff to see the multiple-ohoice queslicns and wiD seal the appropriate section when asked to do so. t will not discuss these questions .. .. College PLACEMENT PLACE AN AP ? NUMBER LABEL _ Board PROGRAM" Iwith anyone at any time after the completion of the multipl_ section. I em awam 01 and agree 10 the Program'. ~ policies and procecilJteS as outlined in the 2003 Buffetin for AP Stt.tdImts and Parents. OR WRITE YOUR AP NUMBER Answer Sheet for May 2003, Form 3ZBP HERE AT EVERY EXAMINATION. PAGE 1 ,...,. W Plintexamination name:.______________________

AP Calc AB 2004 Scoring Guideliens

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Ordinary differential equations

Integral calculus

Differential calculus

Differential topology

derivative

Tangent

Separation of variables

education

AP? Calculus AB 2004 Scoring Guidelines The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT?, the PSAT/NMSQT?, and the Advanced Placement Program? (AP?). The College Board is committed to the principles of

AP Calc AB 2004 Scoring Guidelines (Form B)

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Integral calculus

Analytic geometry

Differential geometry

Tangent

AP? Calculus AB 2004 Scoring Guidelines Form B The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT?, the PSAT/NMSQT?, and the Advanced Placement Program? (AP?). The College Board is committed to the principles of

AP Calc AB 2004 Free Response Questions

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Advanced Placement Calculus

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Advanced Placement Chemistry

AP? Calculus AB 2004 Free-Response Questions The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT?, the PSAT/NMSQT?, and the Advanced Placement Program? (AP?). The College Board is committed to the principles of

AP Calc AB 2003 Free Response Questions (Form B)

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education

Advanced Placement Calculus

Advanced Placement

Advanced Placement Chemistry

AP? Calculus AB 2003 Free-Response Questions Form B These materials were produced by Educational Testing Service? (ETS?), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle. The College Board is a national nonprofit membership association whose mission is to prepare, inspire, and connect students to college and opportunity. Founded in 1900, the association is composed of more than 4,300 schools, colleges, universities, and other educational organizations. Each year, the

The Definite Integral

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