https://www.physicsforums.com/attachment.php?attachmentid=33439&d=1300925084ozlem675 said:How can i show that both limits exist and are equal to 0? I attached limits as bmp file
"i" refers to "i times" not complex number so you can ignore. This formula is calculated after analysis of algortihms by using summations.
No.ozlem675 said:I thought i can solve this limit by L' Hopital's Rule but after derivatives of both parts.
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Can i rewrite log as n^1/2 but I'm not sure about it since the log itself is square root not the "n" nor "2"?
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To prove that both limits exist, you must show that the left-hand limit and the right-hand limit approach the same value. This can be done by evaluating the function at the point in question and showing that as the x-values approach that point from both sides, the y-values approach the same value.
A limit exists for a function if the values of the function approach a specific value as the input values get closer and closer to a given point. This can be thought of as the "instantaneous" value of the function at that point.
To show that a limit is equal to 0, you must first evaluate the function at the point in question and then show that as the input values get closer and closer to that point, the output values approach 0. This can be done by using algebraic manipulations or by graphing the function.
Yes, a graph can be a useful tool to visually show that both limits exist and are equal to 0. By plotting the function and its behavior around the point in question, you can see if the left-hand and right-hand limits approach the same value of 0.
Yes, it is possible for a function to have a limit of 0 but not exist at a certain point. This can happen if the function has a vertical asymptote at that point, meaning that the function approaches infinity as the input values get closer to that point. In this case, the limit would still exist but the function would not be defined at that point.