Explanation Given: The given function is g ( x ) = 4 x . Calculation: Consider the interval to be 1 ≤ t ≤ 1 + h . For h = 0.1 g ′ ( 1 ) ≈ g ( 1.1 ) − g ( 1 ) 1.1 − 1 = [ ( 4 ) 1.1 ] − [ ( 4 ) 1 ] 0.1 = 4.5947 − 4 0.1 = 0.5947 0.1 = 5.947 Thus, the value of g ′ ( 1 ) is 5.947. For h = 0.01 : g ′ ( 1 ) ≈ g ( 1.01 ) − g ( 1 ) 1.01 − 1 = [ ( 4 ) 1

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ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 2.1, Problem 18P

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Evaluate the value of g′(1) by taking smaller and smaller interval.

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Chapter 2.1, Problem 17P

Chapter 2.1, Problem 19P

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Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)

I) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed. J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals. K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.

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Evaluate the value of g ′ ( 1 ) by taking smaller and smaller interval.

Solution Summary: The author evaluates the value of gprime '(1)' by taking smaller and smaller intervals.

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Chapter 2 Solutions