POWER SERIES
... Let f be continuous on the interval a, b .To find the open intervals on which f is increasing or decreasing, use the following steps. 1. Locate the critical numbers of f x in a, b and use these numbers to determine the test intervals. 2. Determine the sign of f ' x at one test value ...
... Let f be continuous on the interval a, b .To find the open intervals on which f is increasing or decreasing, use the following steps. 1. Locate the critical numbers of f x in a, b and use these numbers to determine the test intervals. 2. Determine the sign of f ' x at one test value ...
Word Document - University System of Maryland
... asymptotes, concavity), solutions of maximum and minimum problems, and exponential growth and decay. Explain the uses of Rolle’s Theorem and the Mean Value Theorem. Apply Riemann Sums, the Fundamental Theorem of Calculus, algebraic and trigonometric substitutions, integration by parts, and partial f ...
... asymptotes, concavity), solutions of maximum and minimum problems, and exponential growth and decay. Explain the uses of Rolle’s Theorem and the Mean Value Theorem. Apply Riemann Sums, the Fundamental Theorem of Calculus, algebraic and trigonometric substitutions, integration by parts, and partial f ...
Chapter 4 Section 9 - Columbus State University
... Suppose we are given that F(0) = 1. • We have a place to start—the point (0, 1). • The direction in which we move our pencil is given at each stage by the derivative F’(x) = f (x). ...
... Suppose we are given that F(0) = 1. • We have a place to start—the point (0, 1). • The direction in which we move our pencil is given at each stage by the derivative F’(x) = f (x). ...
log
... 7. The function is continuous, increasing, and one-to-one. 8. The graph is concave downward. D. Examples 1. By comparing areas, show that ln2 <1. ...
... 7. The function is continuous, increasing, and one-to-one. 8. The graph is concave downward. D. Examples 1. By comparing areas, show that ln2 <1. ...
Integral Calculus - Exercises
... 9. It is estimated that t years from now the population of a certain lakeside community will be changing at the rate of 0.6t2 + 0.2t + 0.5 thousand people per year. Environmentalists have found that the level of pollution in the lake increases at the rate of approximately 5 units per 1000 people. By ...
... 9. It is estimated that t years from now the population of a certain lakeside community will be changing at the rate of 0.6t2 + 0.2t + 0.5 thousand people per year. Environmentalists have found that the level of pollution in the lake increases at the rate of approximately 5 units per 1000 people. By ...
Document
... As the function f(x) = (ln x)/x in the example is positive for x > 1, the integral represents the area of the shaded region in this figure. ...
... As the function f(x) = (ln x)/x in the example is positive for x > 1, the integral represents the area of the shaded region in this figure. ...
AP® Calculus AB 2011 Scoring Guidelines Form B
... (a) Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither for the function f. Justify your answer. (b) Find all intervals on which the graph of f is concave down. Justify your answer. (c) Given that f (1) = 2, determine th ...
... (a) Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither for the function f. Justify your answer. (b) Find all intervals on which the graph of f is concave down. Justify your answer. (c) Given that f (1) = 2, determine th ...
Solution - Harvard Math Department
... Solution: We first have to find where the two graphs intersect to determine the integration bounds. They intersect at x = 1 and x = −1. Next, we have to know which function is above and which is below. If we look at x = 0, then we see that f is below. We can see this also from the fact that f is alw ...
... Solution: We first have to find where the two graphs intersect to determine the integration bounds. They intersect at x = 1 and x = −1. Next, we have to know which function is above and which is below. If we look at x = 0, then we see that f is below. We can see this also from the fact that f is alw ...
MATH_125_online_L5__..
... which is uppercase F of x, is going to be equal to the integral so far. So it's going to be the area above the x-axis, minus the area below the x-axis. And it keeps going down until-- once these two areas compensate for each other, the accumulated area function becomes zero because we have the same ...
... which is uppercase F of x, is going to be equal to the integral so far. So it's going to be the area above the x-axis, minus the area below the x-axis. And it keeps going down until-- once these two areas compensate for each other, the accumulated area function becomes zero because we have the same ...
Semester Review
... This is a beginning. It is not intended as a complete review. It is a reminder of the many types of problems we have done this semester and it is a guide for active study. Remember to review old tests and quizzes, problems from the book, and handouts. Pace yourself while studying during the coming w ...
... This is a beginning. It is not intended as a complete review. It is a reminder of the many types of problems we have done this semester and it is a guide for active study. Remember to review old tests and quizzes, problems from the book, and handouts. Pace yourself while studying during the coming w ...
AP Calculus AB - Review for AP Calculus AB Exam (2009).
... LRAM, RRAM, MRAM - rectangular approximation methods - approximate area under curve or value of a definite integral (usually use when given values in a table) Trapezoidal Rule : Recall: A trap ...
... LRAM, RRAM, MRAM - rectangular approximation methods - approximate area under curve or value of a definite integral (usually use when given values in a table) Trapezoidal Rule : Recall: A trap ...
Math 302 Learning Objectives
... o double sigma notation o triple sigma notation o upper sum o lower sum o double integral o integral formula for the volume of a solid bounded between a region Ω in o the xy-plane and the graph of a non-negative function z=f(x,y) defined on Ω. o integral formula for the area of region in a plane o i ...
... o double sigma notation o triple sigma notation o upper sum o lower sum o double integral o integral formula for the volume of a solid bounded between a region Ω in o the xy-plane and the graph of a non-negative function z=f(x,y) defined on Ω. o integral formula for the area of region in a plane o i ...
Antiderivatives - John Abbott College
... In a derivative problem, a function f (x) is given and you find the derivative f ′ (x) using the formulas and rules of derivatives shown in a previous tutorial. In an antiderivative problem, the derivative f ′ (x) is given and you find a function f (x) using the formulas of antiderivatives shown lat ...
... In a derivative problem, a function f (x) is given and you find the derivative f ′ (x) using the formulas and rules of derivatives shown in a previous tutorial. In an antiderivative problem, the derivative f ′ (x) is given and you find a function f (x) using the formulas of antiderivatives shown lat ...
Chapter 4 – Applications of Differentiation
... A physicist who knows the velocity of a particle might wish to know its position at a given time. An engineer who can measure the variable rate at which water is leaking from a tank wants to know the amount leaked over a certain time period. A biologist who knows the rate at which a bacteria populat ...
... A physicist who knows the velocity of a particle might wish to know its position at a given time. An engineer who can measure the variable rate at which water is leaking from a tank wants to know the amount leaked over a certain time period. A biologist who knows the rate at which a bacteria populat ...
