- P.S..1: Let (a) Find (b) Find and (c) Use a graphing utility to approximate...
- P.S..2: Let (a) Use a graphing utility to complete the table. (b) Let Use a...
- P.S..3: In Exercises 3 and 4, (a) write the area under the graph of the giv...
- P.S..4: In Exercises 3 and 4, (a) write the area under the graph of the giv...
- P.S..5: The Fresnel function is defined by the integral (a) Graph the funct...
- P.S..6: The Two-Point Gaussian Quadrature Approximation for is (a) Use this...
- P.S..7: Archimedes showed that the area of a parabolic arch is equal to the...
- P.S..8: Galileo Galilei (15641642) stated the following proposition concern...
- P.S..9: The graph of the function consists of the three line segments joini...
- P.S..10: A car travels in a straight line for 1 hour. Its velocity in miles ...
- P.S..11: Prove x 0 ftx t dt x 0 t 0 fv dv dt. t
- P.S..12: Prove b a fxfx dx 1 2 fb2 fa2. x
- P.S..13: Use an appropriate Riemann sum to evaluate the limit lim n 1 2 3 . ...
- P.S..14: Use an appropriate Riemann sum to evaluate the limit lim n 15 25 35...
- P.S..15: Suppose that is integrable on and for all in the interval Prove tha...
- P.S..16: Let be continuous on the interval where on (a) Show that (b) Use th...
- P.S..17: Verify that by showing the following. (a) (b) (c)n i1 i2 nn 12n 1 6
- P.S..18: Prove that if is a continuous function on a closed interval then b ...
- P.S..19: Let where is shown in the figure. Let and represent the Riemann sum...
- P.S..20: The sine integral function is often used in engineering. The functi...
- P.S..21: Determine the limits of integration where such that has minimal value.
Solutions for Chapter P.S.: Integration
Full solutions for Calculus | 9th Edition
See Inverse cosecant function.
Composition of functions
(f ? g) (x) = f (g(x))
The process of utilizing general information to prove a specific hypothesis
An angle formed by two intersecting planes,
Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.
Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).
Extracting square roots
A method for solving equations in the form x 2 = k.
A series whose terms form a geometric sequence.
The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
Left-hand limit of f at x a
The limit of ƒ as x approaches a from the left.
Length of an arrow
See Magnitude of an arrow.
Magnitude of an arrow
The magnitude of PQ is the distance between P and Q
Angle generated by clockwise rotation.
Two lines that are both vertical or have equal slopes.
Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random
A triangle with a 90° angle.
The y-value of the top of the viewing window.
Zero of a function
A value in the domain of a function that makes the function value zero.