The sequence sqrt(x)*sin(x) does not converge.
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)
The limit does not exist.
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.
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.
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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.
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)
The limit does not exist.
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.
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.
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When the limit of x approaches 0 x approaches the value of x approaches infinity.
Because infinity is not a umber, it is usually not treated as a number when computing functions. Instead, you can look for a limit of a function as it approaches infinity. For example, the limit as x approaches infinity of 1/x is 0. Because sine oscillates, it's value constantly moves up and down, and it's value as it approaches infinity is not defined because it does not converge on any one number, as some other functions (like 1/x) do.
In a square you can see infinity squares. For you to have a limit of squares you have to set a limit of size.
limit x tends to infinitive ((e^x)-1)/(x)
Yes, infinity over zero is considered an indeterminate form. This is because while the numerator approaches infinity, the denominator approaches zero, leading to a situation where the expression does not have a well-defined limit. Depending on the context of the limit, the result can vary significantly, making it indeterminate rather than a fixed value.