Calculus Review Semester 1

Final review priority assignment: Calculus Fall study Guide #1,2,4,5,7,17,28,31,32,35,41,45,47,48,52,55,61-66, 73,74,78,80-82,92,94 Unit 4 Suduko – good additional study if desired

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

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

(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.

*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