CK-12-Pre-Calculus Concepts

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

You can verify the limit in the table.

TABLE14.8:

x f(x)

.75 2.3125

.9 2.71

.99 2.9701

.999 2.997

1 Error

1.001 3.003

1.01 3.0301

1.1 3.31

1.25 3.8125

2. limx→ 2 f(x) = 1

TABLE14.9:

x 1.75 1.9 1.99 1.999 2 2.001 2.01 2.1 2.25

f(x) 0.75 0.9 0.99 0.999 Error 1.001 1.01 1.1 1.25

3. limx→ 0 f(x) = 0

TABLE14.10:

x -0.1 -0.01 -0.001 0.001 0.01 0.1

f(x) 0.20526 0.02005 0.002 -0.002 -0.02 -0.1952

Practice

Estimate the following limits numerically.

1. 
   

   limx→ 5 x^2 x−−^255

   
   


2. 
   

   limx→− 1 x^2 −x+^3 x 1 −^4

   
   


3. 
   

   limx→ 2 x^3 −x (^25) −x^23 +x+^2 x 2 −^4

   
   


4. 
   

   limx→ 0

   
   

√x+ 2 −√ 2

x

5. limx→ 3

( 1

x− 3 −x^29 − 9

)