Estimate Limits Numerically

Exercises 1.2
6 & 8



Question 6

The purpose of this table is to see what happens as we get closer and closer to 3. I say x cannot be the number in the middle of the table or 3. I will not evaluate this function at the given x-values here. I just want to know if my reasoning is correct.

Note: The graph tells a different story. I think x tends to -3 not 3. You say?



Question 8

The purpose of this table is to see what happens as we get closer and closer to 3. I say x cannot be the number in the middle of the table or 3. I will not evaluate this function at the given x-values here. I just want to know if my reasoning is correct.

Note: The graph tells a different story. Does x really tend to 3?

 

reasoning is correct

6.
if you calculate this way, as x->3 limit will be undefined
table
x ........... 2.9 ........... 2.99 ........... 2.999 ........... 3 ........... 3.001 ........... 3.01 ........... 3.1
f(x) ........ 0.17 ........ 0.17 ........ 0.167 ........ (undefined) ........ 0.167 ........ 0.167 ........ 0.16

but, if you simplify function you got y=1/(x+3),
table
x ........... 2.9 ... ........ 2.99 ........... 2.999 ........... 3 ........... 3.001 ........... 3.01 ........... 3.1
f(x) ........ 0.17 ........ 0.167........ 0.16669........ (1/6) ........ 0.16666 ........ 0.166 ........ 0.164

then as x->3 limit will be 1/6

 

8.









so

when you do the table, you see as x->3 that f(x)=-1/16

 

Using the table is very tedious. This exercise is basically to show students how to find the limit as x tends to a certain value without actually getting there.

 

When it has a minus sign at the top it means that you must find the limit when the desired x comes from the left, meaning that you must find which number the limit goes as x becomes more closer to 3 from the left.

 

Yes, I figured that out by reading your reply twice.