- #1
lizzie
- 25
- 0
find
lim (-1)^[x]
x->2
[x] is the greatest integer function
-> means tends to
thanks to any help.
lim (-1)^[x]
x->2
[x] is the greatest integer function
-> means tends to
thanks to any help.
lizzie said:find
lim (-1)^[x]
x->2
[x] is the greatest integer function
-> means tends to
thanks to any help.
lizzie said:find
lim (-1)^[x]
x->2
[x] is the greatest integer function
-> means tends to
thanks to any help.
The limit of (-1)^[x] as x approaches 2 does not exist. This is because the greatest integer function is not continuous at x = 2 and therefore the limit does not exist.
The greatest integer function, also known as the floor function, rounds any number down to the nearest integer. This means that as x approaches 2 from the left side, the function will output -2 and as x approaches 2 from the right side, the function will output -1. Since the left and right limits do not equal each other, the overall limit does not exist.
No, the limit of (-1)^[x] and the limit of (-1)^x are not the same. The limit of (-1)^x as x approaches 2 does exist and is equal to -1. This is because the exponential function is continuous at x = 2.
Yes, the greatest integer function can be applied to any number. It will always round the number down to the nearest integer.
The graph of the greatest integer function consists of a series of horizontal lines, with the value of the function changing only at integer values of x. The line y = -1 represents the function at x = 2, with a discontinuity at this point. The rest of the graph is filled with lines representing the output of the function for all other values of x.