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# Solutions for Chapter 2.5: Implicit Differentiation ## Full solutions for Calculus | 8th Edition

ISBN: 9780618502981 Solutions for Chapter 2.5: Implicit Differentiation

Solutions for Chapter 2.5
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##### ISBN: 9780618502981

Calculus was written by and is associated to the ISBN: 9780618502981. This textbook survival guide was created for the textbook: Calculus, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: Implicit Differentiation includes 80 full step-by-step solutions. Since 80 problems in chapter 2.5: Implicit Differentiation have been answered, more than 83850 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Conjugate axis of a hyperbola

The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

• Cubic

A degree 3 polynomial function

• Dot product

The number found when the corresponding components of two vectors are multiplied and then summed

• Index

• Instantaneous velocity

The instantaneous rate of change of a position function with respect to time, p. 737.

• Intermediate Value Theorem

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

• Linear combination of vectors u and v

An expression au + bv , where a and b are real numbers

• Matrix, m x n

A rectangular array of m rows and n columns of real numbers

• Median (of a data set)

The middle number (or the mean of the two middle numbers) if the data are listed in order.

• Normal distribution

A distribution of data shaped like the normal curve.

• Positive linear correlation

See Linear correlation.

• Reciprocal identity

An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

• Removable discontinuity at x = a

lim x:a- ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

• 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.

• Scientific notation

A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• Standard position (angle)

An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive x-axis

• Trigonometric form of a complex number

r(cos ? + i sin ?)

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

• Vertical asymptote

The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.

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