define limt of a function at a point and give two examples
Answers
Step-by-step explanation:
Informally, a function f assigns an output f(x) to every input x. We say the function has a limit L at an input p: this means f(x) gets closer and closer to L as x moves closer and closer to p. More specifically, when f is applied to any input sufficiently close to p, the output value is forced arbitrarily close to L.
Limits of Functions
The limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a.a. The concept of a limit is the fundamental concept of calculus and analysis. It is used to define the derivative and the definite integral, and it can also be used to analyze the local behavior of functions near points of interest.
Informally, a function is said to have a limit LL at aa if it is possible to make the function arbitrarily close to LL by choosing values closer and closer to aa. Note that the actual value at aa is irrelevant to the value of the limit.
The notation is as follows:
\lim_{x \to a} f(x) = L,
x→a
lim
f(x)=L,
which is read as "the limit of f(x)f(x) as xx approaches aa is L.L."
The limit of \( f(x) \) at \(x_0\) is the \(y\)-coordinate of the red point, not \(f(x_0).\)
The limit of f(x)f(x) at x_0x
0
is the yy-coordinate of the red point, not f(x_0).f(x
0
). [1]