Calculus Review Final S1

Note: Key handouts are attached.

Final Review sites to add to paper review.

https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/trapezoidal-approximation-of-area-under-curve

https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/e/using-rectangles-to-approximate-area-under-a-curve

https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/generalizing-a-left-riemann-sum-with-equally-spaced-rectangles

(remember how to use left & right Riemann Sums)

http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx

https://www.youtube.com/watch?v=JKXgOIJ_N9E

http://analyzemath.com/calculus/Problems/area_rectangle_triangle.html

http://www.themathpage.com/aCalc/max.htm

http://www.mathcaptain.com/calculus/concavity.html

http://tutorial.math.lamar.edu/Classes/CalcI/AvgFcnValue.aspx

https://mathispower4u.wordpress.com/2013/07/08/ex-definite-integrals-as-area-given-a-graph-function/

http://www.understandingcalculus.com/chapters/04/4-2.php

https://www.maths.usyd.edu.au/u/UG/JM/MATH1111/Quizzes/index.html

*Challenge problems (Solved in teams during class.):

*1)Find the tangent line and normal line to the curve 2x +4x²y-y²=26 at (2,1)

(a normal line is perpendicular to a tangent line)

https://math.stackexchange.com/questions/521630/find-equation-of-tangent-and-normal-lines-differentiation

*Graph to confirm your answers.

y-1=-9/7(x-2), y-1=7/9(x-2)

*2) You are designing a rectangular poster to contain and area of 144 square units of printing with a 2 inch margin at the top and bottom of the frame and a 4 inch margin on the sides. What are the overall dimensions of the paper used?

http://www-groups.mcs.st-and.ac.uk/~vince/teaching/spring04/a10.pdf

**https://socratic.org/questions/a-rectangle-is-inscribed-with-its-base-on-the-x-axis-and-its-upper-corners-on-th-2

Slope of a curve at a point:

https://socratic.org/calculus/derivatives/slope-of-a-curve-at-a-point

https://www.varsitytutors.com/ap_calculus_ab-help/slope-of-a-curve-at-a-point

Limit of function including one sided limits:

http://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx

Concavity

**https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingsol2directory/GraphingSol2.html#SOLUTION%209 (note problem #9)

horizontal asymptote

http://www.softschools.com/math/calculus/finding_horizontal_asymptotes_of_rational_functions/

Also, check the limit by checking a point near the value of the limit.

Differentiable at a vertical tangent line, corner, or cusp:

http://www-personal.umich.edu/~ojwalch/michael-mackenzie/index.html

Normal line perpendicular of Tangent line

Average rate of change

https://www.khanacademy.org/math/algebra/algebra-functions/average-rate-of-change-word-problems/a/average-rate-of-change-review

Find derivative to show that the average rate of change of f(x)=4x^3+3x^2 over the interval [1,3].

https://socratic.org/questions/how-do-you-find-the-average-rate-of-change-of-y-x-3-1-from-x-1-to-x-3

Find the function whose derivative is f’(x)=4x+2 whose graph passes through (2,3).

https://socratic.org/questions/find-the-function-with-the-given-derivative-whose-graph-passes-through-the-point

Find the equation of a tangent line at a point.

Definition of a derivative – recognize it in a MC question

Mean value theorem – recognize it in a MC question

Maximums, Minimums

Definite and indefinite integrals

Average value (integrals)

http://tutorial.math.lamar.edu/Classes/CalcI/AvgFcnValue.aspx

Free Response: Reimann’s Sum

*https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap17-calculus-ab-q1.pdf

**Use plastic paper & back covers of text on final.

--No Calculator 1-26 question -- Calculator portion 27-33, Free Response

ADDITIONAL REVIEW

https://www.youtube.com/watch?v=WlBpPpE-XRg

Maximum area:

http://www.math-prof.com/Calculus_1/Calc_Ch_15.asp

Rate of change

http://www.analyzemath.com/calculus/Problems/rate_change.html

https://www.khanacademy.org/math/differential-calculus/derivative_applications/rates_of_change/v/rates-of-change-between-radius-and-area-of-circle

https://www.khanacademy.org/math/differential-calculus/derivative_applications/rates_of_change/v/rate-of-change-of-balloon-height#!

https://www.khanacademy.org/math/differential-calculus/derivative_applications/rates_of_change/v/related-rates-of-water-pouring-into-cone

https://www.khanacademy.org/math/differential-calculus/derivative_applications/rates_of_change/e/related-rates

http://www.analyzemath.com/calculus/Problems/maximum_volume_problem.html

Linearization

http://tutorial.math.lamar.edu/Classes/CalcI/LinearApproximations.aspx

https://www.youtube.com/watch?v=8STdGfdeTMs

(first part of video – not the general solution)

http://tutorial.math.lamar.edu/Problems/CalcI/LinearApproximations.aspx

numbers 2 & 3

Derivative ln

http://www.intmath.com/differentiation-transcendental/5-derivative-logarithm.php

http://www.themathpage.com/acalc/exponential.htm

(scroll down to problem 3)

Point closest to curve

http://math.stackexchange.com/questions/967268/finding-the-closest-distance-between-a-point-a-curve

http://www.enotes.com/homework-help/find-point-curve-y-x-2-closest-point-3-4-342346