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Calculus Differentiation and Limit Techniques

Learn about differentiation, limits, chain rule, tangent and normal lines, implicit differentiation, trigonometric differentiation, antiderivatives, continuity, critical points, inflection points, and more in calculus. Master multiple choice exams and problem solving techniques.

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Calculus Differentiation and Limit Techniques

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  1. Differentiation 3.4 Chain Rule 3.1 Poly&exp 3.2 Prod&Quo Types of Q The slope of the tangent line to the curve The slope of the normal line to the curve An equation of the tangent line An equation of the normal line 3.3 Trig 3.11 Hyp 3.5 Implicit Diff Implicit Diff 3.5 Inv. Trig 3.6 Log Diff variables appear in the base and exponent

  2. ANTIDIFFERENTIATION

  3. ANTIDIFFERENTIATION F141 F143 F122

  4. Limit and L’H number 1 Evaluate Number/0 1) 2) 1)common denominator 2)rationalization (conjugate) 3)common factor 3) 4) 2 squeeze

  5. Limit and L’H F083 121 F143

  6. Continuity F141 F132 F151

  7. Five theorems 1)Newton’s method 2)Roll’s thm 3)MVT 4)EVT 5)IVT

  8. Critical Points Inflection Points 1)Critical points 1)Inflection points domain domain

  9. Local Max or Min Absolute Max or Min 1)Critical points 2)Evaluate : (original function f(x) ) 1)Critical points 2) Study the sign domain domain Max Min

  10. Increasing Concave up or down 1) 2)Study the sign : 1)Critical points 2) Study the sign domain domain ‘

  11. 8)Maximize or Minimize(WE1) I)What Max or min Look for the word: Largest Smallest Shortest Minimum maximum III)1variable Use the given quantity information to write a relation between two variables II)EquationWrite A =area V=volume P=product S=distance Equation in two or more variables

  12. Limit and L’H number 1 Evaluate Number/0 1) 2) 1)common denominator 2)rationalization (conjugate) 3)common factor 3) 4) 2 squeeze

  13. 1) Newton’s method

  14. 2)Critical Points Find Domain First

  15. 3)Absolute Max,Min (M,m)

  16. 4)local Max,Min

  17. 5)Increasing, Decreasing

  18. 6)Concave, up-down f cont at c

  19. 7)Inflection points

  20. 9)MeanValue or Rolle’s

  21. 10) Anti-drivative

  22. 11) L’Hospital 1)common denominator, or 2)rationalization (conjugate) 3)common factor

  23. 12) Linear Approximation

  24. 13) Memorize

  25. Multiple choice Exam 1) Skim all 28 problems to select these you know then mark them Look for the keyword: local , inc, concave, inflection, Newton,….. 2) Start by solving these problems (keep bubbling at the end) you have 180min/28Prob = 6.4min each 3) Eliminate answers that are wrong 4) Try working backwards. Plug the answers into the question to see if they make sense

  26. Multiple choice Exam 4) If you have absolutely no idea what the answer is, can't use any of the above techniques, choose one letter 1) Pattern: Look for similarities

  27. Multiple choice Exam

  28. Use your knowledge in Graph

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