Directions; Solve each integral below using one of the following methods: Change of Variables Geometric Formula Improper Integrals Parts Partial Fraction.

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Differential Equations

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Presentation transcript:

Directions; Solve each integral below using one of the following methods: Change of Variables Geometric Formula Improper Integrals Parts Partial Fraction U-substitution Methods of Integration Review

ModelExponentialLogistic Differential Equation General Solution 8.A certain wild animal preserve can support no more than 250 gorillas. In 1970, 28 gorillas were known to be in the preserve. Assume that the rate of growth of population is dP/dt = (250 − P)P, where t is in years. Find a formula for the gorilla population in terms of t; then, determine how long it will take for the gorilla population to reach the carrying capacity of the preserve. What is the gorilla population when the rate of change of the population is maximized? 7.The rate of increase of the population of Springfield is proportional to the population at any given time. If the population in 1950 was 50,000 and in 1980 it was 75,000, what is the expected population in the year 2010? When will Springfield’s population reach 1,000,000 people? Justify your answers. Directions: Complete the table below (look it up if you have to) & complete the problems Growth Review

Slope Formula for Polar Coordinates Area Formula for Polar Coordinates Substitution to use to integrate sin 2  Substitution to use to integrate cos 2  9. Polar Equations Review

Directions: List the next three non-zero terms as well as the general term for each Maclaurin Series Series Review Directions: List the first three four terms as the general term for each any Maclaurin Series and for any Taylor series about x = a

Slope Formula for Parametric Equations Speed Formula for Parametric Equations Acceleration Formula for Parametric Equations Distance Formula for Parametric Equations 19. Parametric Equations Review