mat251_093_final_guide

mat251_093_final_guide - • Properly apply the properties...

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mat 251 – calculus for life sciences fall 2009 mat 251 / final exam / study guide This list is not necessarily exhaustive. Any topic covered in lecture or homework is fair game for the test. As the final is cumulative, you should also refer back to the study guides for the three midterm exams. Compare and contrast: Antiderivative vs. derivative, substitution vs. the chain rule, integration by parts vs. the product rule, definite vs. indefinite integral, and converge vs. diverge. Discuss the link between velocity, area, and distance. (Distance = Velocity x Time) Given the number of bars to use, find a simple (left- or right-hand) Riemann sum to estimate the area under the curve between two values. Explain the connection between a definite integral and an infinite sum. () ( ) ⎟ Δ = = n i i n b a t t f dt t f 1 lim Find antiderivatives of polynomials, rational functions, exponentials, and trig functions.
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Unformatted text preview: • Properly apply the properties of antiderivatives. • Know the formula for integration by parts. du v v u dv u ∫ ∫ − ⋅ = • Understand the relationship between position (s), velocity (v), and acceleration (a). • Apply the fundamental theorem of calculus to solve definite integrals. ( ) ( ) ( ) ( ) a F b F t F dt t f b a b a − = = ∫ • Calculate the area between two curves using integration. • Evaluate improper integrals using limits. • Discuss the scenarios that cause an improper integral to be divergent. practice problems Section Assigned / Practice More Practice 5.2 2-10 even, 18, 20, 24 16, 22, 28 5.3 18, 42, 80, 82 6-14e, 70, 84, 88, 91, 92 5.4 16, 22, 36 2, 8, 10, 24, 28, 38-40 5.5 74 64, 76 5.6 40, 42 34 5.9 6, 16, 24, 47 18, 22, 38, 40...
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