 1.1.1: Find the two numbers that have distance 3 from 1 by (a) measuring t...
 1.1.2: Find all pairwise distances between the numbers 5, 2, and 7 by (a) ...
 1.1.3: Solve the following equations: (a) 2x 4 = 6 (b) x 3 = 2 (c) 2x...
 1.1.4: Solve the following equations: (a) 2x + 4 = 5x 2 (b) 5 3u = ...
 1.1.5: Solve the following inequalities: (a) 5x 2 4 (b) 1 3x > 8 (c) ...
 1.1.6: Solve the following inequalities: (a) 2x + 3 < 6 (b) 3 4x 2 (c)...
 1.1.7: In 742, determine the equation of the line that satisfies the state...
 1.1.8: In 742, determine the equation of the line that satisfies the state...
 1.1.9: In 742, determine the equation of the line that satisfies the state...
 1.1.10: In 742, determine the equation of the line that satisfies the state...
 1.1.11: In 742, determine the equation of the line that satisfies the state...
 1.1.12: In 742, determine the equation of the line that satisfies the state...
 1.1.13: In 742, determine the equation of the line that satisfies the state...
 1.1.14: In 742, determine the equation of the line that satisfies the state...
 1.1.15: In 742, determine the equation of the line that satisfies the state...
 1.1.16: In 742, determine the equation of the line that satisfies the state...
 1.1.17: In 742, determine the equation of the line that satisfies the state...
 1.1.18: In 742, determine the equation of the line that satisfies the state...
 1.1.19: In 742, determine the equation of the line that satisfies the state...
 1.1.20: In 742, determine the equation of the line that satisfies the state...
 1.1.21: In 742, determine the equation of the line that satisfies the state...
 1.1.22: In 742, determine the equation of the line that satisfies the state...
 1.1.23: In 742, determine the equation of the line that satisfies the state...
 1.1.24: In 742, determine the equation of the line that satisfies the state...
 1.1.25: In 742, determine the equation of the line that satisfies the state...
 1.1.26: In 742, determine the equation of the line that satisfies the state...
 1.1.27: In 742, determine the equation of the line that satisfies the state...
 1.1.28: In 742, determine the equation of the line that satisfies the state...
 1.1.29: In 742, determine the equation of the line that satisfies the state...
 1.1.30: In 742, determine the equation of the line that satisfies the state...
 1.1.31: In 742, determine the equation of the line that satisfies the state...
 1.1.32: In 742, determine the equation of the line that satisfies the state...
 1.1.33: In 742, determine the equation of the line that satisfies the state...
 1.1.34: In 742, determine the equation of the line that satisfies the state...
 1.1.35: In 742, determine the equation of the line that satisfies the state...
 1.1.36: In 742, determine the equation of the line that satisfies the state...
 1.1.37: In 742, determine the equation of the line that satisfies the state...
 1.1.38: In 742, determine the equation of the line that satisfies the state...
 1.1.39: In 742, determine the equation of the line that satisfies the state...
 1.1.40: In 742, determine the equation of the line that satisfies the state...
 1.1.41: In 742, determine the equation of the line that satisfies the state...
 1.1.42: In 742, determine the equation of the line that satisfies the state...
 1.1.43: To convert a length measured in feet to a length measured in centim...
 1.1.44: (a) To convert the weight of an object from kilograms (kg) to pound...
 1.1.45: Assume that the distance a car travels is proportional to the time ...
 1.1.46: Assume that the number of seeds a plant produces is proportional to...
 1.1.47: Experimental study plots are often squares of length 1 m. If 1 ft c...
 1.1.48: Large areas are often measured in hectares (ha) or in acres. If 1 h...
 1.1.49: To convert the volume of a liquid measured in ounces to a volume me...
 1.1.50: To convert a distance measured in miles to a distance measured in k...
 1.1.51: Car speed in many countries is measured in kilometers per hour. In ...
 1.1.52: (a) The Celsius scale is devised so that 0C is the freezing point o...
 1.1.53: (a) The Kelvin (K) scale is an absolute scale of temperature. The z...
 1.1.54: Use the following steps to show that if two nonvertical lines l1 an...
 1.1.55: Find the equation of a circle with center (1, 4) and radius 3.
 1.1.56: Find the equation of a circle with center (2, 3) and radius 4.
 1.1.57: (a) Find the equation of a circle with center (2, 5) and radius 3. ...
 1.1.58: (a) Find all possible radii of a circle centered at (3, 6) so that ...
 1.1.59: Find the center and the radius of the circle given by the equation ...
 1.1.60: Find the center and the radius of the circle given by the equation ...
 1.1.61: Find the center and the radius of the circle given by the equation ...
 1.1.62: Find the center and the radius of the circle given by the equation ...
 1.1.63: (a) Convert 75 to radian measure. (b) Convert 17 12 to degree measure.
 1.1.64: (a) Convert 15 to radian measure. (b) Convert 3 4 to degree measure.
 1.1.65: Evaluate the following expressions without using a calculator: (a) ...
 1.1.66: Evaluate the following expressions without using a calculator: (a) ...
 1.1.67: (a) Find the values of [0, 2) that satisfy sin = 1 2 _ 3 (b) Find t...
 1.1.68: (a) Find the values of [0, 2) that satisfy cos = 1 2 _ 2 (b) Find t...
 1.1.69: Show that the identity 1 + tan2 = sec2 follows from sin2 + cos2 = 1
 1.1.70: Show that the identity 1 + cot2 = csc2 follows from sin2 + cos2 = 1
 1.1.71: Solve 2 cos sin = sin on [0, 2).
 1.1.72: Solve sec2 x = _ 3 tan x + 1 on [0, ).
 1.1.73: Evaluate the following exponential expressions: (a) 4342/3 (b) 3231...
 1.1.74: Evaluate the following exponential expressions: (a) (2423/2)2 (b) _...
 1.1.75: Which real number x satisfies (a) log4 x = 2? (b) log1/3 x = 3? (c)...
 1.1.76: Which real number x satisfies (a) log1/2 x = 4? (b) log1/4 x = 2? (...
 1.1.77: Which real number x satisfies (a) log1/2 32 = x? (b) log1/3 81 = x?...
 1.1.78: Which real number x satisfies (a) log4 64 = x? (b) log1/5 625 = x? ...
 1.1.79: Simplify the following expressions: (a) ln 1 3 (b) log4(x2 4) (c) l...
 1.1.80: Simplify the following expressions: (a) ln 1 5 (b) ln x2y2 x (c) lo...
 1.1.81: Solve for x. (a) e3x1 = 2 (b) e2x = 10 (c) ex21 = 10
 1.1.82: Solve for x. (a) 3x = 81 (b) 92x+1 = 27 (c) 105x = 1000
 1.1.83: Solve for x. (a) ln(x 3) = 5 (b) ln(x + 2) + ln(x 2) = 1 (c) log3 x...
 1.1.84: Solve for x. (a) ln(2x 3) = 0 (b) log2(1 x) = 3 (c) ln x3 2 ln x = ...
 1.1.85: In 8592, simplify each expression and write it in the standard form...
 1.1.86: In 8592, simplify each expression and write it in the standard form...
 1.1.87: In 8592, simplify each expression and write it in the standard form...
 1.1.88: In 8592, simplify each expression and write it in the standard form...
 1.1.89: In 8592, simplify each expression and write it in the standard form...
 1.1.90: In 8592, simplify each expression and write it in the standard form...
 1.1.91: In 8592, simplify each expression and write it in the standard form...
 1.1.92: In 8592, simplify each expression and write it in the standard form...
 1.1.93: In 9398, let z = 3 2i , u = 4 + 3i , v = 3 + 5i , and w = 1 i . Com...
 1.1.94: In 9398, let z = 3 2i , u = 4 + 3i , v = 3 + 5i , and w = 1 i . Com...
 1.1.95: In 9398, let z = 3 2i , u = 4 + 3i , v = 3 + 5i , and w = 1 i . Com...
 1.1.96: In 9398, let z = 3 2i , u = 4 + 3i , v = 3 + 5i , and w = 1 i . Com...
 1.1.97: In 9398, let z = 3 2i , u = 4 + 3i , v = 3 + 5i , and w = 1 i . Com...
 1.1.98: In 9398, let z = 3 2i , u = 4 + 3i , v = 3 + 5i , and w = 1 i . Com...
 1.1.99: If z = a + bi, find z + z and z z.
 1.1.100: If z = a + bi, find z. Use your answer to compute (z), and compare ...
 1.1.101: In 101106, solve each quadratic equation in the complex number syst...
 1.1.102: In 101106, solve each quadratic equation in the complex number syst...
 1.1.103: In 101106, solve each quadratic equation in the complex number syst...
 1.1.104: In 101106, solve each quadratic equation in the complex number syst...
 1.1.105: In 101106, solve each quadratic equation in the complex number syst...
 1.1.106: In 101106, solve each quadratic equation in the complex number syst...
 1.1.107: In 107112, first determine whether the solutions of each quadratic ...
 1.1.108: In 107112, first determine whether the solutions of each quadratic ...
 1.1.109: In 107112, first determine whether the solutions of each quadratic ...
 1.1.110: In 107112, first determine whether the solutions of each quadratic ...
 1.1.111: In 107112, first determine whether the solutions of each quadratic ...
 1.1.112: In 107112, first determine whether the solutions of each quadratic ...
 1.1.113: Show (z) = z.
 1.1.114: Show z + w = z + w.
 1.1.115: Show zw = z w.
Solutions for Chapter 1.1: Preliminaries
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 1.1: Preliminaries
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus For Biology and Medicine (Calculus for Life Sciences Series), edition: 3. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688. Since 115 problems in chapter 1.1: Preliminaries have been answered, more than 20914 students have viewed full stepbystep solutions from this chapter. Chapter 1.1: Preliminaries includes 115 full stepbystep solutions.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Demand curve
p = g(x), where x represents demand and p represents price

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

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Horizontal line
y = b.

Leibniz notation
The notation dy/dx for the derivative of ƒ.

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

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Position vector of the point (a, b)
The vector <a,b>.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Radicand
See Radical.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Solve by elimination or substitution
Methods for solving systems of linear equations.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Sum of an infinite series
See Convergence of a series

Symmetric property of equality
If a = b, then b = a

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Tangent
The function y = tan x