 5.4.1: (a) Write the sum in two ways:12 +14 +16 +18 = 4k=1= 3j=0(b) Expres...
 5.4.2: Express the sums in closed form.(a) nk=1k (b) nk=1(6k + 1) (c) nk=1k2
 5.4.3: Divide the interval [1, 3] into n = 4 subintervals of equallength.(...
 5.4.4: Find the left endpoint approximation for the area betweenthe curve ...
 5.4.5: The right endpoint approximation for the net signed areabetween y =...
 5.4.6: 38 Write each expression in sigma notation but do not evaluate. 1 +...
 5.4.7: 38 Write each expression in sigma notation but do not evaluate. 1 3...
 5.4.8: 38 Write each expression in sigma notation but do not evaluate. 1 1...
 5.4.9: (a) Express the sum of the even integers from 2 to 100 insigma nota...
 5.4.10: Express in sigma notation.(a) a1 a2 + a3 a4 + a5(b) b0 + b1 b2 + b3...
 5.4.11: 1116 Use Theorem 5.4.2 to evaluate the sums. Check youranswers usin...
 5.4.12: 1116 Use Theorem 5.4.2 to evaluate the sums. Check youranswers usin...
 5.4.13: 1116 Use Theorem 5.4.2 to evaluate the sums. Check youranswers usin...
 5.4.14: 1116 Use Theorem 5.4.2 to evaluate the sums. Check youranswers usin...
 5.4.15: 1116 Use Theorem 5.4.2 to evaluate the sums. Check youranswers usin...
 5.4.16: 1116 Use Theorem 5.4.2 to evaluate the sums. Check youranswers usin...
 5.4.17: 1720 Express the sums in closed form. nk=13kn
 5.4.18: 1720 Express the sums in closed form. n1k=1k2n
 5.4.19: 1720 Express the sums in closed form. n1k=1k3n2
 5.4.20: 1720 Express the sums in closed form. n1k=1k3n2
 5.4.21: 2124 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.4.22: 2124 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.4.23: 2124 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.4.24: 2124 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.4.25: (a) Write the first three and final two summands in thesum nk=12 + ...
 5.4.26: For a function f that is continuous on [a, b], Definition5.4.5 says...
 5.4.27: 2730 Divide the specified interval into n = 4 subintervals ofequal ...
 5.4.28: 2730 Divide the specified interval into n = 4 subintervals ofequal ...
 5.4.29: 2730 Divide the specified interval into n = 4 subintervals ofequal ...
 5.4.30: 2730 Divide the specified interval into n = 4 subintervals ofequal ...
 5.4.31: 3134 Use a calculating utility with summation capabilities ora CAS ...
 5.4.32: 3134 Use a calculating utility with summation capabilities ora CAS ...
 5.4.33: 3134 Use a calculating utility with summation capabilities ora CAS ...
 5.4.34: 3134 Use a calculating utility with summation capabilities ora CAS ...
 5.4.35: 3540 Use Definition 5.4.3 with xk as the right endpoint ofeach subi...
 5.4.36: 3540 Use Definition 5.4.3 with xk as the right endpoint ofeach subi...
 5.4.37: 3540 Use Definition 5.4.3 with xk as the right endpoint ofeach subi...
 5.4.38: 3540 Use Definition 5.4.3 with xk as the right endpoint ofeach subi...
 5.4.39: 3540 Use Definition 5.4.3 with xk as the right endpoint ofeach subi...
 5.4.40: 3540 Use Definition 5.4.3 with xk as the right endpoint ofeach subi...
 5.4.41: 4144 Use Definition 5.4.3 with xk as the left endpoint of eachsubin...
 5.4.42: 4144 Use Definition 5.4.3 with xk as the left endpoint of eachsubin...
 5.4.43: 4144 Use Definition 5.4.3 with xk as the left endpoint of eachsubin...
 5.4.44: 4144 Use Definition 5.4.3 with xk as the left endpoint of eachsubin...
 5.4.45: 4548 Use Definition 5.4.3 with xk as the midpoint of eachsubinterva...
 5.4.46: 4548 Use Definition 5.4.3 with xk as the midpoint of eachsubinterva...
 5.4.47: 4548 Use Definition 5.4.3 with xk as the midpoint of eachsubinterva...
 5.4.48: 4548 Use Definition 5.4.3 with xk as the midpoint of eachsubinterva...
 5.4.49: 4952 Use Definition 5.4.5 with xk as the right endpoint ofeach subi...
 5.4.50: 4952 Use Definition 5.4.5 with xk as the right endpoint ofeach subi...
 5.4.51: 4952 Use Definition 5.4.5 with xk as the right endpoint ofeach subi...
 5.4.52: 4952 Use Definition 5.4.5 with xk as the right endpoint ofeach subi...
 5.4.53: (a) Show that the area under the graph of y = x3 and overthe interv...
 5.4.54: Find the area between the graph of y = x and the interval[0, 1]. [H...
 5.4.55: An artist wants to create a rough triangular design usinguniform sq...
 5.4.56: An artist wants to create a sculpture by gluing together uniformsph...
 5.4.57: 5760 Consider the sum4k=1[(k + 1)3 k3]=[53 43]+[43 33]+ [33 23]+[23...
 5.4.58: 5760 Consider the sum4k=1[(k + 1)3 k3]=[53 43]+[43 33]+ [33 23]+[23...
 5.4.59: 5760 Consider the sum4k=1[(k + 1)3 k3]=[53 43]+[43 33]+ [33 23]+[23...
 5.4.60: 5760 Consider the sum4k=1[(k + 1)3 k3]=[53 43]+[43 33]+ [33 23]+[23...
 5.4.61: (a) Show that11 3 +13 5 ++1(2n 1)(2n + 1) = n2n + 1Hint:1(2n 1)(2n ...
 5.4.62: (a) Show that11 2 +12 3 +13 4 ++1n(n + 1) = nn + 1Hint:1n(n + 1) = ...
 5.4.63: Let x denote the arithmetic average of the n numbersx1, x2,...,xn. ...
 5.4.64: LetS = nk=0arkShow that S rS = a arn+1 and hence thatnk=0ark = a ar...
 5.4.65: By writing out the sums, determine whether the followingare valid i...
 5.4.66: Which of the following are valid identities?(a) ni=1aibi = ni=1aini...
 5.4.67: Prove part (c) of Theorem 5.4.1.
 5.4.68: Prove Theorem 5.4.4.
 5.4.69: Writing What is net signed area? How does this conceptexpand our ap...
 5.4.70: Writing Based on Example 6, one might conjecture thatthe midpoint a...
Solutions for Chapter 5.4: THE DEFINITION OF AREA AS A LIMIT; SIGMA NOTATION
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 5.4: THE DEFINITION OF AREA AS A LIMIT; SIGMA NOTATION
Get Full SolutionsSince 70 problems in chapter 5.4: THE DEFINITION OF AREA AS A LIMIT; SIGMA NOTATION have been answered, more than 39965 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 5.4: THE DEFINITION OF AREA AS A LIMIT; SIGMA NOTATION includes 70 full stepbystep solutions.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Distributive property
a(b + c) = ab + ac and related properties

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

Gaussian curve
See Normal curve.

Horizontal line
y = b.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Linear system
A system of linear equations

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Monomial function
A polynomial with exactly one term.

Multiplicative inverse of a matrix
See Inverse of a matrix

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Response variable
A variable that is affected by an explanatory variable.

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

Secant line of ƒ
A line joining two points of the graph of ƒ.

Slope
Ratio change in y/change in x

Sum of an infinite series
See Convergence of a series