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 FunctionsThe standard rule for finding the limit of a composite function looks something like this:Rule for Limits of Composite FunctionsIf lim g(x) = K and f(x) is continuous at x = K, then lim ƒ (g(x)) = ƒ (limg(x)).x→ax→aWe will expand upon the idea of continuity later in the unit. For now, think of f(x) is continuous at x = K iff(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 functionis 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 thefollowing limits.-1+00a.) lim f(f(x))x→1c.) limg(f(x))y = f(z)-10b.) limf(g(x))5y = g(x)67i

a)limx→1f(fx) limx→1f(fx)=flimx→1fx ⇒f(3) =2 limx→1ffx=2

Answered: Example 2: Consider the graphs of the…

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

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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Question

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.

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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