Evaluate the limits using a table of values. Given , find:
I. ii. iii.
A) i. -1 ii. -1 Iii. -1
B) i. 1 ii. 1 Iii. 1
C) i. 1 ii. -1 Iii.
D) i. -1 ii. 1 Iii.

Question

Evaluate the limits using a table of values. Given  , find:
I.  ii.  iii. 
A) i. -1 ii. -1 Iii. -1 
B) i. 1 ii. 1 Iii. 1 
C) i. 1 ii. -1 Iii. 
D) i. -1 ii. 1 Iii.

Quizplus · Accepted Answer

We can use a table of values to evaluate the limits. 
For values of x close to 0, sin(x) and cos(x) are both close to 0, and x^2 is very small. Therefore, we can estimate that the limit is approximately 
(1 - cos(x))/x^2 = 1/2

Using the table of values:
i. x = 0.1, (1 - cos(x))/x^2 = 0.497
ii. x = 0.01, (1 - cos(x))/x^2 = 0.500
iii. x = 0.001, (1 - cos(x))/x^2 = 0.500

All values are approximately 1/2, which is equivalent to 0.5. 
Therefore, the answer is choice C, i. 1, ii. -1, iii. -1.

Evaluate the Limits Using a Table of Values