As X approaches infinity it approaches close as you like to 0.
so, sin(-1/2)
The limit of cos2(x)/x as x approaches 0 does not exist. As x approaches 0 from the left, the limit is negative infinity. As x approaches 0 from the right, the limit is positive infinity. These two values would have to be equal for a limit to exist.
limit x tends to infinitive ((e^x)-1)/(x)
The sequence sqrt(x)*sin(x) does not converge.
The limit does not exist.
1
The limit of cos2(x)/x as x approaches 0 does not exist. As x approaches 0 from the left, the limit is negative infinity. As x approaches 0 from the right, the limit is positive infinity. These two values would have to be equal for a limit to exist.
limit x tends to infinitive ((e^x)-1)/(x)
What is the limit as x approaches infinity of the square root of x? Ans: As x approaches infinity, root x approaches infinity - because rootx increases as x does.
The sequence sqrt(x)*sin(x) does not converge.
The limit does not exist.
1
When the limit as the function approaches from the left, doesn't equal the limit as the function approaches from the right. For example, let's look at the function 1/x as x approaches 0. As it approaches 0 from the left, it travels towards negative infinity. As it approaches 0 from the right, it travels towards positive infinity. Therefore, the limit of the function as it approaches 0 does not exist.
It is undefined. In infinities and infinitessimals we use limits, so we see trends as we approach a limit. However this gives different answers, The limit as A approaches infinity of A x 0 is 0. But the limit as B approaches zero of infinty x B is infinite. To be well-defined both of these answers need to be the same.
When the limit of x approaches 0 x approaches the value of x approaches infinity.
Anything to the power of 1 is that same something, so infinity to the power of 1 is infinity. Keep in mind that infinity is a conceptual thing, often expressed as a limit as something approaches a boundary condition of the domain of a function. Without thinking of limits, infinity squared is still infinity, so the normal rules of math would seem to not apply.
The limit is 0.
The "value" of the function at x = 2 is (x+2)/(x-2) so the answer is plus or minus infinity depending on whether x approaches 2 from >2 or <2, respectively.