Explanation Procedure used: Addition or Subtraction of Rational Numbers (Fraction) with unlike denominators: 1. Compute the LCD of the denominators. 2. Write fraction with the LCD as the denominator. 3. Add or subtract the numerators and write the result over the common denominator. 4. Write the result in lowest terms. “ Finding the lowest common denominator ( LCD ) : 1. Find the prime factors of each denominator. 2. For each different prime factor that appears, note the highest power to which it is raised in any one of the denominators. 3. Form the product of all the different prime factors, each raised to the power found in step 2. This product is called the lowest common denominator.” Calculation: The given function is f ( x ) = 2 x 2 + 4 . Substitute x = x + h in f ( x ) to find the value of f ( x + h ) as, f ( x + h ) = 2 ( x + h ) 2 + 4 Substitute f ( x ) and f ( x + h ) values in the expression f ( x + h ) − f ( x ) to detrmine the value of f ( x + h ) − f ( x ) . f ( x + h ) − f ( x ) = 2 ( x + h ) 2 + 4 − 2 x 2 + 4 = 2 x 2 + h 2 + 2 x h + 4 − 2 x 2 + 4 Note that, the denominators of the above fractional expression are different. To make the denominators of the fractions equivalent, find the LCD of the denominators. The factor of x 2 + h 2 + 2 x h + 4 is x 2 + h 2 + 2 x h + 4 . The factor of x 2 + 4 is x 2 + 4 . Therefore, x 2 + h 2 + 2 x h + 4 and x 2 + 4 are the factors of the LCD. Thus, the LCD of the denominators of each fractions is the product of x 2 + h 2 + 2 x h + 4 and x 2 + 4 that is ( x 2 + h 2 + 2 x h + 4 ) . To make the resulting denominator in each fraction equal to the LCD, multiply and divide the fraction by the proper quantity

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 6.6, Problem 50E

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The expression f(x+h)−f(x) for the function f(x)=2x2+4 and then simplify it.

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Chapter 6.6, Problem 49E

Chapter 6.6, Problem 51E

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Determine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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The expression f ( x + h ) − f ( x ) for the function f ( x ) = 2 x 2 + 4 and then simplify it.

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The expression f(x+h)−f(x) for the function f(x)=2x2+4 and then simplify it.

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Chapter 6 Solutions