Explanation Limit Laws: Suppose that c is a constant and the limits lim x → a f ( x ) and lim x → a g ( x ) exist, then Limit law 8: lim x → a x = a Direct substitution property: If f is a polynomial or a rational function and a is in the domain of f , then lim x → a f ( x ) = f ( a ) . Fact 1: If f ( x ) = g ( x ) when x ≠ a , then lim x → a f ( x ) = lim x → a g ( x ) , provided the limit exist. Let f ( h ) = ( − 5 + h ) 2 − 25 h (1) Note 1: The direct substitution method is not applicable for the function f ( h ) since letting h = 0 , the function f ( 0 ) is in indeterminate form. f ( 0 ) = ( − 5 + 0 ) 2 − 25 0 = 25 − 25 0 = 0 0 Note 2: The Quotient rule is not applicable for the function f ( h ) as the limit of the denominator is zero. lim h → 0 ( h ) = 0 ( by limit law 8 ) Note 3: “ The limit may be infinite or it may be some finite value when both the numerator and the denominator approach 0.” Calculation: By note 3, take the limit h approaches zero but h ≠ 0 , Simplify f ( h ) by using elementary algebra

2nd Edition

ISBN: 9781133490975

Author: Stewart, James

Publisher: Cengage Learning

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 1.4, Problem 17E

To determine

To evaluate: The limit of the function limh→0(−5+h)2−25h.

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Chapter 1.4, Problem 16E

Chapter 1.4, Problem 18E

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Chapter 1 Solutions

Essential Calculus

Ch. 1.1 - 1. If f(x)=x+2x and g(u)=u+2u, is it true that f =...Ch. 1.1 - If f(x)=x2xx1andg(x)=x is it true that f = g?Ch. 1.1 - The graph of a function f is given. (a) State the...Ch. 1.1 - The graphs of f and g are given. (a) State the...Ch. 1.1 - Prob. 5E Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Prob. 9E Ch. 1.1 - The graph shows the height of the water in a...

Ch. 1.1 - Prob. 11E Ch. 1.1 - Sketch a rough graph of the number of hours of...Ch. 1.1 - Prob. 13E Ch. 1.1 - Sketch a rough graph of the market value of a new...Ch. 1.1 - Prob. 15E Ch. 1.1 - You place a frozen pie in an oven and bake it for...Ch. 1.1 - A homeowner mows the lawn every Wednesday...Ch. 1.1 - An airplane takes off from an airport and lands an...Ch. 1.1 - If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a),...Ch. 1.1 - A spherical balloon with radius r inches has...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Prob. 24E Ch. 1.1 - Find the domain of the function. 31. f(x)=x+4x29 Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Find the domain of the function. 37. F(p)=2p Ch. 1.1 - Find the domain and range and sketch the graph of...Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 34E Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - Prob. 49E Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - A cell phone plan has a basic charge of 35 a...Ch. 1.1 - In a certain country, income tax is assessed as...Ch. 1.1 - The functions in Example 6 and Exercises 52 and...Ch. 1.1 - Graphs of f and g are shown. 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The limit of the function lim h → 0 ( − 5 + h ) 2 − 25 h .

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To evaluate: The limit of the function limh→0(−5+h)2−25h.

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Chapter 1 Solutions