Complete the table

Question

Complete the table by computing f(x) at the given values of x.

f(x) = 1
x − 3
x	2.9	2.99	2.999	3.001	3.01	3.1
f(x)

Use these results to estimate the indicated limit (if it exists). (If an answer does not exist, enter DNE.)

lim x→3 f(x)

 

Answer 1

Hi Meena,

it is enough replace given x in the function f(x) = x - 3

x = 2.9 f( x ) = 2.9 - 3 = - .1

x = 2.9 9 f( x ) = 2.9 9 - 3 = - .01

x = 2.999 f( x ) = 2.999 - 3 = - .001

x = 3.001 f( x ) = 3.001 - 3 = .001

x = 3.01 f( x ) = 3.01 - 3 = .01

x = 3.1 f( x ) = 3.1 - 3 = - .1

You see, all numbers are very close to the ZERO so, the limit of f(x) = x - 3 when x goes to the 3 will be ZERO. On the other word the limit of function exists and equals ZERO.

I hope it is useful,

Minoo