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# Solutions for Chapter 1.2: INITIAL-VALUE PROBLEMS ## Full solutions for A First Course in Differential Equations with Modeling Applications | 10th Edition

ISBN: 9781111827052 Solutions for Chapter 1.2: INITIAL-VALUE PROBLEMS

Solutions for Chapter 1.2
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##### ISBN: 9781111827052

A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. Chapter 1.2: INITIAL-VALUE PROBLEMS includes 51 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since 51 problems in chapter 1.2: INITIAL-VALUE PROBLEMS have been answered, more than 49902 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Acceleration due to gravity

g ? 32 ft/sec2 ? 9.8 m/sec

• Average velocity

The change in position divided by the change in time.

• Base

See Exponential function, Logarithmic function, nth power of a.

• Combinations of n objects taken r at a time

There are nCr = n! r!1n - r2! such combinations,

• Constraints

See Linear programming problem.

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Demand curve

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

• Frequency distribution

See Frequency table.

• Histogram

A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

• Identity function

The function ƒ(x) = x.

• Inverse cotangent function

The function y = cot-1 x

• Inverse relation (of the relation R)

A relation that consists of all ordered pairs b, a for which a, b belongs to R.

• Left-hand limit of f at x a

The limit of ƒ as x approaches a from the left.

• Linear equation in x

An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

• Logarithmic function with base b

The inverse of the exponential function y = bx, denoted by y = logb x

• Major axis

The line segment through the foci of an ellipse with endpoints on the ellipse

• Permutations of n objects taken r at a time

There are nPr = n!1n - r2! such permutations

• Rational zeros theorem

A procedure for finding the possible rational zeros of a polynomial.

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

• xz-plane

The points x, 0, z in Cartesian space.

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