- 9-2.Q1: Differentiate: y = x tan x
- 9-2.Q2: Integrate: x10 dx
- 9-2.Q3: Sketch: y = ex
- 9-2.Q4: Integrate: cos 3x dx
- 9-2.Q5: Differentiate: y = cos 5x sin 5x
- 9-2.Q6: Sketch: y = 2/x
- 9-2.Q7: r(x) = t(x) dx if and only if ?.
- 9-2.Q8: Definition: (x) = ?
- 9-2.Q9: If f(6.2) = 13, f(6.5) = 19, and f(6.8) = 24, then (6.5) ?
- 9-2.Q10: If region R (Figure 9-2b) is rotated about the line x = c, the volu...
- 9-2.1: For 1-10, integrate by parts x sin x dx
- 9-2.2: For 1-10, integrate by parts x cos 3x dx
- 9-2.3: For 1-10, integrate by parts xe4x dx
- 9-2.4: For 1-10, integrate by parts 6x e3x dx
- 9-2.5: For 1-10, integrate by parts (x + 4)e5x dx
- 9-2.6: For 1-10, integrate by parts (x + 7)e2x d
- 9-2.7: For 1-10, integrate by parts x3 ln x dx
- 9-2.8: For 1-10, integrate by parts x5 ln 3x d
- 9-2.9: For 1-10, integrate by parts x2 ex dx
- 9-2.10: For 1-10, integrate by parts x2 ex dx
- 9-2.11: Integral of the Natural Logarithm Problem: You can evaluate the int...
- 9-2.12: Rapid Repeated Integration by Parts
Solutions for Chapter 9-2: Integration by PartsA Way to Integrate Products
Full solutions for Calculus: Concepts and Applications | 2nd Edition
An angle whose measure is between 0° and 90°
Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point
The two separate curves that make up a hyperbola
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable
a + b = b + a ab = ba
The function y = cot x
Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists
An identity involving a trigonometric function of u - v
Difference of two vectors
<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>
Domain of a function
The set of all input values for a function
equation of a hyperbola
(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1
Explicitly defined sequence
A sequence in which the kth term is given as a function of k.
Points that satisfy the constraints in a linear programming problem.
Future value of an annuity
The net amount of money returned from an annuity.
A visible representation of a numerical or algebraic model.
Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x - c) (x - z 2) Á (x - z n)
Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,
Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.
See n factorial.