- #1
Nowshin
- 4
- 0
Homework Statement
lim (1/sqrt(x+a)-1/sqrt x)
x->0
Homework Equations
None
The Attempt at a Solution
Too many too be listed :P
statdad said:Attempted solutions: "Too many too be listed "
Aaah, there's a (not the, as there may be others) rub - you need to show something you've tried before you receive any help. What types of things have you attempted?
Pacopag said:Sometimes, a limit just doesn't exist. But you have to prove that it doesn't. I'm sure that you've determined that the first term is fine. So your problem arises in the second term. I think that a proof by induction using L'Hospitale's rule should do it (I mean repeated applications of the rule just make things worse and worse).
The limit of a complex expression is the value that the expression approaches as the independent variable approaches a certain value. It can also be thought of as the value that the expression "approaches" but does not necessarily reach.
Exploring the limit of a complex expression is important because it helps us understand the behavior of the expression at certain points and can also help us solve problems involving rates of change and optimization.
The limit of a complex expression can be determined by using various techniques such as algebraic manipulation, graphing, and evaluating the expression at different values of the independent variable.
Some common types of limits in complex expressions include one-sided limits, limits at infinity, and limits involving trigonometric or logarithmic functions.
Yes, there can be restrictions on the values that the independent variable can approach in a limit of a complex expression. These restrictions are typically mentioned in the problem or can be inferred from the context of the expression.