 4.2.1: In Exercises 16, find the sum. Use the summation capabilities of a ...
 4.2.3: In Exercises 16, find the sum. Use the summation capabilities of a ...
 4.2.4: In Exercises 16, find the sum. Use the summation capabilities of a ...
 4.2.5: In Exercises 16, find the sum. Use the summation capabilities of a ...
 4.2.6: In Exercises 16, find the sum. Use the summation capabilities of a ...
 4.2.7: In Exercises 714, use sigma notation to write the sum.1 51 1 52 1 5...
 4.2.8: In Exercises 714, use sigma notation to write the sum.9 1 1 9 1 2 9...
 4.2.9: In Exercises 714, use sigma notation to write the sum.7 1 6 5 7 2 6...
 4.2.10: In Exercises 714, use sigma notation to write the sum.1 1 4 2 1 2 4...
 4.2.11: In Exercises 714, use sigma notation to write the sum.2 n 3 2 n 2 n...
 4.2.12: In Exercises 714, use sigma notation to write the sum.1 2 n 1 2 2 n...
 4.2.13: In Exercises 714, use sigma notation to write the sum.2 1 3 n 2 3 n...
 4.2.14: In Exercises 714, use sigma notation to write the sum.1 n 1 0 n 2 ....
 4.2.15: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.16: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.17: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.18: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.19: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.20: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.21: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.22: In Exercises 1522, use the properties of summation and Theorem 4.2 ...
 4.2.23: In Exercises 23 and 24, use the summation capabilities of a graphin...
 4.2.24: In Exercises 23 and 24, use the summation capabilities of a graphin...
 4.2.25: Consider the function (a) Estimate the area between the graph of an...
 4.2.26: Consider the function (a) Estimate the area between the graph of an...
 4.2.27: In Exercises 2732, use left and right endpoints and the given numbe...
 4.2.28: In Exercises 2732, use left and right endpoints and the given numbe...
 4.2.29: In Exercises 2732, use left and right endpoints and the given numbe...
 4.2.30: In Exercises 2732, use left and right endpoints and the given numbe...
 4.2.31: In Exercises 2732, use left and right endpoints and the given numbe...
 4.2.32: In Exercises 2732, use left and right endpoints and the given numbe...
 4.2.33: In Exercises 3336, bound the area of the shaded region by approxima...
 4.2.34: In Exercises 3336, bound the area of the shaded region by approxima...
 4.2.35: In Exercises 3336, bound the area of the shaded region by approxima...
 4.2.36: In Exercises 3336, bound the area of the shaded region by approxima...
 4.2.37: In Exercises 37 40, find the limit ofsn 81 n4 n2 n 12 4 s
 4.2.38: In Exercises 37 40, find the limit ofsn 64 n3 nn 12n 1 6
 4.2.39: In Exercises 37 40, find the limit ofsn 18 n2 nn 1 2 s
 4.2.40: In Exercises 37 40, find the limit ofsn 1 n2 nn 1 2 s
 4.2.41: In Exercises 4144, use upper and lower sums to approximate the area...
 4.2.42: In Exercises 4144, use upper and lower sums to approximate the area...
 4.2.43: In Exercises 4144, use upper and lower sums to approximate the area...
 4.2.44: In Exercises 4144, use upper and lower sums to approximate the area...
 4.2.45: In Exercises 4548, use the summation formulas to rewrite the expres...
 4.2.46: In Exercises 4548, use the summation formulas to rewrite the expres...
 4.2.47: In Exercises 4548, use the summation formulas to rewrite the expres...
 4.2.48: In Exercises 4548, use the summation formulas to rewrite the expres...
 4.2.49: lim n n i1 24i n2
 4.2.50: lim n n i1 2i n 2 n l
 4.2.51: lim n n i1 1 n3 i 12 l
 4.2.52: lim n n i1 1 2i n 2 2 n li
 4.2.53: lim n n i1 1 i n 2 n
 4.2.54: lim n n i1 1 2i n 3 2 n l
 4.2.55: Consider a triangle of area 2 bounded by the graphs of and (a) Sket...
 4.2.56: Consider a trapezoid of area 4 bounded by the graphs of and (a) Ske...
 4.2.57: In Exercises 5766, use the limit process to find the area of the re...
 4.2.58: In Exercises 5766, use the limit process to find the area of the re...
 4.2.59: In Exercises 5766, use the limit process to find the area of the re...
 4.2.60: In Exercises 5766, use the limit process to find the area of the re...
 4.2.61: In Exercises 5766, use the limit process to find the area of the re...
 4.2.62: In Exercises 5766, use the limit process to find the area of the re...
 4.2.63: In Exercises 5766, use the limit process to find the area of the re...
 4.2.64: In Exercises 5766, use the limit process to find the area of the re...
 4.2.65: In Exercises 5766, use the limit process to find the area of the re...
 4.2.66: In Exercises 5766, use the limit process to find the area of the re...
 4.2.67: In Exercises 6772, use the limit process to find the area of the re...
 4.2.68: In Exercises 6772, use the limit process to find the area of the re...
 4.2.69: In Exercises 6772, use the limit process to find the area of the re...
 4.2.70: In Exercises 6772, use the limit process to find the area of the re...
 4.2.71: In Exercises 6772, use the limit process to find the area of the re...
 4.2.72: In Exercises 6772, use the limit process to find the area of the re...
 4.2.73: In Exercises 7376, use the Midpoint Rule with to approximate the ar...
 4.2.74: In Exercises 7376, use the Midpoint Rule with to approximate the ar...
 4.2.75: In Exercises 7376, use the Midpoint Rule with to approximate the ar...
 4.2.76: In Exercises 7376, use the Midpoint Rule with to approximate the ar...
 4.2.77: fx x, 0, 4 x
 4.2.78: fx 2, 6 8 x2 1 , f
 4.2.79: fx tan 1, 3 x 8 , f
 4.2.80: fx cos x, 0, 2] f
 4.2.81: In Exercises 81 and 82, determine which value best approximates the...
 4.2.82: In Exercises 81 and 82, determine which value best approximates the...
 4.2.83: In your own words and using appropriate figures, describe the metho...
 4.2.84: In your own words and using appropriate figures, describe the metho...
 4.2.85: Consider the region bounded by the graphs of and as shown in the fi...
 4.2.86: Consider a function that is increasing on the interval The interval...
 4.2.87: In Exercises 87 and 88, determine whether the statement is true or ...
 4.2.88: In Exercises 87 and 88, determine whether the statement is true or ...
 4.2.89: Use the figure to write a short paragraph explaining why the formul...
 4.2.90: Consider an sided regular polygon inscribed in a circle of radius ...
 4.2.91: The table lists the measurements of a lot bounded by a stream and t...
 4.2.92: A child places cubic building blocks in a row to form the base of a...
 4.2.93: Prove each formula by mathematical induction. (You may need to revi...
 4.2.94: A dart, thrown at random, hits a square target. Assuming that any t...
Solutions for Chapter 4.2: Area
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 4.2: Area
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 93 problems in chapter 4.2: Area have been answered, more than 63720 students have viewed full stepbystep solutions from this chapter. Calculus was written by and is associated to the ISBN: 9780547167022. This textbook survival guide was created for the textbook: Calculus , edition: 9. Chapter 4.2: Area includes 93 full stepbystep solutions.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

Interval
Connected subset of the real number line with at least two points, p. 4.

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Modulus
See Absolute value of a complex number.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Rose curve
A graph of a polar equation or r = a cos nu.

Spiral of Archimedes
The graph of the polar curve.

Trigonometric form of a complex number
r(cos ? + i sin ?)