Calculus Tutorial 2.6.006

 
Problem Statement

{6,7,8,9}

Plot the graphs of

and

on the same set of axes. Compute if f(x) is squeezed by l(x) and u(x) at .

 
Step 1

Recall what it means for f to be squeezed by l and u and how we can apply the Squeeze Theorem to find limits.

Question 1

The function f is squeezed at x = c if there exist two functions l and u such that l(x) ≤ f(x) ≤ u(x) for all x ≠ c in an open interval containing c. Then if

we must have

.

This is called the Squeeze Theorem.

Incorrect.
Correct.

 
Step 2

Question Sequence

Question 2

Note that is always zero.

Based on the graphing techniques of shifting, stretching and reflecting, it has the shape of an absolute value graph y = |x| shifted π/2 units to the and 9 units .

Incorrect.
Correct.

 
Step 3

Use the Squeeze Theorem to find if f(x) is squeezed by l(x) and u(x) at x = π/2.

In order to use the Squeeze Theorem, we would need to show that . Then by the Squeeze Theorem, would also be equal to L.

Question Sequence

Question 5

Either from the graph in Step 2, or the continuity of the functions, find and .

Incorrect.
Correct.