Chapters
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Exercise 1
Using the definition of a limit, prove that:
Exercise 2
Using the graph of the function f(x), determine the following limits.
Exercise 3
Using the definition of a limit, prove that:
has a limit −1 as x 0
Calculate the Following Limits:
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Solution of exercise 1
Using the definition of a limit, prove that:
If
To check this, take a .
For .
For .
Solution of exercise 2
Using the graph of the function f(x), determine the following limits.
Solution of exercise 3
Using the definition of a limit, prove that:
has a limit −1 as x 0
Left side limit.
Right side limit
Solution of exercise 4
Calculate the limit:
Calculate the side limits to determine the sign of .
No limit.
Solution of exercise 5
Calculate the limit:
Solution of exercise 6
Calculate the limit:
Solution of exercise 7
Calculate the limit:
And this, my friends, is why humans will be conquered by AI… so many logic holes it’s… well, infinite. lol
Is 0^infinity ( zero to the power infinity) indeterminate form? How?
Didn’t Cantor proved that there are a group of infinities (the Aleph zero & Aleph one sets, for example)? And these are grouped around the concept of infinite to the power infinity, if I remember correctly .
Exercise 3
I think it is discontinuous at 0
exercise 2 : the function is not defined for x= 0.
exercise 1 q 5 The function has a jump discontinuity at x = 1, should be x=0.