- 1.1: One of the legs of a right triangle has length 4 cm. Express the le...
- 1.2: The altitude perpendicular to the hypotenuse of a right triangle is...
- 1.3: Solve the equation | 2x 2 1 | 2 | x 1 5 | 3.
- 1.4: Solve the inequality | x 2 1 | 2 | x 2 3 | > 5.
- 1.5: Sketch the graph of the function fsxd | x 2 2 4| x | 1 3|.
- 1.6: Sketch the graph of the function tsxd | x 2 2 1 | 2 | x 2 2 4 |.
- 1.7: Draw the graph of the equation x 1 | x | y 1 | y |.
- 1.8: Sketch the region in the plane consisting of all points sx, yd such...
- 1.9: The notation maxha, b, . . .j means the largest of the numbers a, b...
- 1.10: Sketch the region in the plane defined by each of the following equ...
- 1.11: Evaluate slog2 3dslog3 4dslog4 5d slog31 32d.
- 1.12: (a) Show that the function fsxd ln( x 1 sx 2 1 1 ) is an odd functi...
- 1.13: Solve the inequality lnsx 2 2 2x 2 2d < 0.
- 1.14: Use indirect reasoning to prove that log2 5 is an irrational number
- 1.15: A driver sets out on a journey. For the first half of the distance ...
- 1.16: . Is it true that f 8 s t 1 hd f 8 t 1 f 8 h?
- 1.17: Prove that if n is a positive integer, then 7n 2 1 is divisible by 6.
- 1.18: Prove that 1 1 3 1 5 1 1 s2n 2 1d n2 .
- 1.19: If f0sxd x 2 and fn11sxd f0s fnsxdd for n 0, 1, 2, . . . , find a f...
- 1.20: (a) If f0sxd 1 2 2 x and fn11 f0 8 fn for n 0, 1, 2, . . . , find a...
Solutions for Chapter 1: Calculus 8th Edition
Full solutions for Calculus | 8th Edition
See Inverse tangent function.
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable
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
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers
See Right circular cone.
Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)
Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space
Explicitly defined sequence
A sequence in which the kth term is given as a function of k.
The points (x, y, z) in space with x > 0 y > 0, and z > 0.
The numbers . . ., -3, -2, -1, 0,1,2,...2
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0
A boxplot with the outliers removed.
Negative linear correlation
See Linear correlation.
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.
A set of ordered pairs of real numbers.
Solve by substitution
Method for solving systems of linear equations.
An identity involving a trigonometric function of u + v
A set of equations or inequalities.
Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.
The points x, y, 0 in Cartesian space.