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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Graphing and Visualizing Limits Exercises

Example 1

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches 0?

Example 2

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches 2π?

Example 3

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches π / 2?

Example 4

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches -π?

Example 5

Let f(x) = x2 -4x + 3. Graph f(x) and use the graph to find the limit of f(x) as x approaches 0.

Example 6

Let f(x) = x2 -4x + 3. Graph f(x) and use the graph to find the limit of f(x) as x approaches 3.

Example 7

Let f(x) = x2 -4x + 3. Graph f(x) and use the graph to find the limit of f(x) as x approaches 1.

Example 8

Although we say "the limit of f(x) as x approaches 2 is 5," we write

limx → 2 f(x) = 5.

Let f(x) = 2 – 2x. Find the limit, limx → 2 f(x).

Example 9

Let f(x) = 2 – 2x. Find the limit, limx → 0 f(x).

Example 10

Let f(x) = 2 - 2x. Find the limit, limx → 1 f(x).