Find the following limits if they exist
1. Iim x -> 4
(1)/(x-4)
2. lim x -> 0
sin 1/x
3. lim x -> 1 f(x) if f(x) {x+2 if x = 1, 2x2-1 if x >1
4. Consider f(x) = (x+3)/(|x+3|)
a. lim x -> -3- f(x) =
b. lim x -> -3+ f(x) =
c. lim x -> -3 f(x) =
+128408
1. Iim x -> 4
(1)/(x-4)
This limit will not exist.....as x approaches 4 from the left the function becomes increasingly more negative......as x approaches 4 from the right, the function becomes increasingly more positive
Here's a graph to show this :
https://www.desmos.com/calculator/sxf0xscp3a
+128408 2. lim x -> 0
sin ( 1/x )
This limit does not exist ....see the graph here :
https://www.desmos.com/calculator/apbhkqpybo
+128408 3. lim x -> 1 f(x) if f(x) {x+2 if x = 1, 2x^2 - 1 if x >1
When x approaches 1 from the left, f(x) = (1) + 2 = 3
When x approaches 1 from the right, f(x) = 2(1)^2 - 1 = 1
So.....this limit does not exist as x approaches 1 because both limits would have to be the same approaching from the left and the right
