CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 14. Concepts of Calculus

Example A
Complete the table and use the result to estimate the limit.
limx→ 2 x 2 x−−x^2 − 2

TABLE14.2:

x 1.9 1.99 1.999 2.001 2.01 2.1

f(x)

Solution:While it is not necessary to use the table feature in the calculator, it is very efficient. Another option is to
substitute the givenxvalues into the expressionx 2 x−−x^2 − 2 and record your results.

TABLE14.3:

x 1.9 1.99 1.999 2.001 2.01 2.1

f(x) 0.34483 0.33445 0.33344 0.33322 0.33223 0.32258

The evidence suggests that the limit is^13.
Example B
Complete the table and use the result to estimate the limit.
limx→ 2 xx 2 −−^24

TABLE14.4:

x 1.9 1.99 1.999 2.001 2.01 2.1

f(x)

Solution:You can trick the calculator into giving a very exact answer by typing in 1.999999999999 because then
the calculator rounds instead of producing an error.

TABLE14.5:

x 1.9 1.99 1.999 2.001 2.01 2.1

f(x) 0.25641 0.25063 0.25006 0.24994 0.24938 0.2439

The evidence suggests that the limit is^14.
Example C
Complete the table and use the result to estimate the limit.