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Example 2: Consider the graphs of the functions f(x) and g(x) given below. Find each of the following limits. -1 0 a.) lim f(f(x)) c.) limg(f(x)) y = f(z) ZZ -2 b.) limf(g(x)) y = g(x)

Example 2: Consider the graphs of the functions f(x) and g(x) given below. Find each of the following limits. -1 0 a.) lim f(f(x)) c.) limg(f(x)) y = f(z) ZZ -2 b.) limf(g(x)) y = g(x)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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What is the answer to the letters a, b, and c? What is the solution to the answer? Thanks!

Operations on Limits and Limits of Composite Functions The standard rule for finding the limit of a composite function looks something like this: Rule for Limits of Composite Functions If lim g(x) = K and f(x) is continuous at x = K, then lim ƒ (g(x)) = ƒ (limg(x)). x→a x→a We will expand upon the idea of continuity later in the unit. For now, think of f(x) is continuous at x = K if f(x) has no holes, breaks or asymptotes at x = K. While useful, this rule can be very problematic if the inner function's limit does not exist or if the outer function is not continuous at the value of the inner function's limit.
Transcribed Image Text:Operations on Limits and Limits of Composite Functions The standard rule for finding the limit of a composite function looks something like this: Rule for Limits of Composite Functions If lim g(x) = K and f(x) is continuous at x = K, then lim ƒ (g(x)) = ƒ (limg(x)). x→a x→a We will expand upon the idea of continuity later in the unit. For now, think of f(x) is continuous at x = K if f(x) has no holes, breaks or asymptotes at x = K. While useful, this rule can be very problematic if the inner function's limit does not exist or if the outer function is not continuous at the value of the inner function's limit.
Example 2: Consider the graphs of the functions f(x) and g(x) given below. Find each of the following limits. -1 +0 0 a.) lim f(f(x)) x→1 c.) limg(f(x)) y = f(z) -1 0 b.) limf(g(x)) 5 y = g(x) 6 7 i
Transcribed Image Text:Example 2: Consider the graphs of the functions f(x) and g(x) given below. Find each of the following limits. -1 +0 0 a.) lim f(f(x)) x→1 c.) limg(f(x)) y = f(z) -1 0 b.) limf(g(x)) 5 y = g(x) 6 7 i
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