$$\lim_{x \to +\infty} \sqrt{x^2+3}-x$$karush said:[tex]\lim_{x\to +\infty}\sqrt{x^2+3}-x}[/tex]
sorry first of all how do you turn this string into latex
I don't see the icon tool on the editor
thnx
karush & edit said:[tex]\lim_{x\to +\infty}{(\sqrt{x^2 + 3} - x)}[/tex]
A limit with square root is a mathematical concept that describes the behavior of a function as the input approaches a certain value, often written as "limit x→a f(x)" where "x" is the input and "a" is the value the input approaches. The limit with square root specifically involves a square root function within the function being evaluated.
To evaluate a limit with square root, you can use algebraic manipulation or graphical analysis. Algebraically, you can simplify the function and then plug in the value the input approaches to find the limit. Graphically, you can plot the function and observe the behavior as the input approaches the given value.
A one-sided limit with square root only considers the behavior of the function as the input approaches the given value from one side (either the left or the right). A two-sided limit with square root considers the behavior from both sides and only exists if the one-sided limits are equal.
Yes, a limit with square root can be undefined if the function has a vertical asymptote at the given value or if the one-sided limits do not exist or are not equal.
Limits with square root have many real-world applications in fields such as physics, engineering, and economics. For example, they can be used to model the behavior of natural phenomena such as radioactive decay, the growth of populations, and the spread of diseases. They are also used in optimization problems to find the maximum or minimum values of a function.