1210 – Final Review
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The final is comprehensive, covering chapters 1-5 (with the exception of sections
3.7, 4.6 and 5.7).
NO calculators will be allowed for this exam.
You should bring your uID.
Scratch Paper will be provided.
You may bring a 5x8 index card of notes (on both sides, if you want) to use as a
reference. Make sure it’s truly a 5x8 index card and not something that closely
resembles a 5x8 index card. If you need one, I can provide one for you.
Course Objectives covered on this Exam:
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compute limits of algebraic and trigonometric functions in one variable and identify
when the limit does not exist.
use limits to discuss the continuity of a function in one variable and identify
asymptotes of a function in one variable.
compute derivatives of algebraic and trigonometric functions in one variable both
explicitly and implicitly.
analyze a graph using understanding of derivatives and limits.
apply knowledge of derivatives to solve problems (linear approximation, related
rate, optimization).
compute indefinite and definite integrals of some algebraic and trigonometric
functions in one variable.
apply knowledge of integrals to solve problems (area, volume, length, surface area,
work, centers of mass).
explain the relationship between derivatives and integrals.
Topics
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Limits
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As x goes to a finite number
As x goes to infinity
Trig functions
Asymptotes
Continuity
Definition of Derivative
Definition of Definite Integral
 Special sum formulas
Derivatives
o Constant Function Rule
o Identity Function Rule
o Power Rule
o Constant Multiple Rule
o Sum/Difference Rule
o Product Rule
o Quotient Rule
o Trig Derivatives
o Chain Rule
o Higher-Order Derivatives
Implicit Differentiation
Analyze graph
 asymptotes (vertical, horizontal and oblique)
 critical Points (end, stationary and singular points)
 increasing/decreasing (first derivative sign line)
 min/max points
 concavity (second derivative sign line)
 inflection points
 sketch graphs
o MVT for Derivatives
o Derivative Application type problems
 Related Rates
 Differentials/Approximations
 Optimization problems
• Integration
o Indefinite Integrals (Antiderivatives)
o Power Rule
o Trig Rules
o U-substitution
o Fundamental Theorem of Calculus
 Derivatives of Definite Integrals
 Evaluating Definite Integrals
o Definite Integrals
o MVT for Integrals
o Integration Application type problems
 Solve Differential Equations
 Average Value of a Function
 Area of a bounded 2D region
 Volumes of revolution
• Washer/Disk Method
• Shell Method
 Arc Length of a smooth curve
 Surface Area of a solid
 Work
 Moments & Center of mass
Some Additional Practice Problems:
Chapter 1 Review
Sample Test (p. 91) #2-24 even, 32, 34, 36
Chapter 2 Review
Sample Test (p. 148-149) #1, 6-28 even, 34-46 even, 41
Chapter 3 Review
Sample Test (p. 210-213) #2-36 even, 40, 42, 45, 49-52 all, 54-74 even
Chapter 4 Review
Sample Test (p. 271-273) #1-29 odd, 16, 22
Chapter 5 Review
Sample Test (p. 322-323) #1-6 all, 8, 11, 12, 15, 16, 18-23 all
Don’t Forget about the review problems posted on the website.
I would also recommend using the past midterms, quizzes, and homework assignments when
reviewing for the final.
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