Don't you mean 0 ≤ f(x) ≤ 1?thatguythere said:Homework Statement
Suppose 0 ≤ f(x) ≥ 1 for all x, find lim x→0 x^4f(x)
thatguythere said:Homework Equations
The Attempt at a Solution
I'm very uncertain about how to go about doing this.
lim x→0 x^4 f(x) = 0^4 (0)
= 0
lim x→0 x^4 f(x) = 1^4 (1)
=1
How does that prove anything?
Finding a limit when assigned restrictions to f(x) means determining the value that a function approaches as the input (x) gets closer and closer to a specific point, or when certain conditions or limitations are placed on the function.
A limit exists when the function approaches the same value from both sides of the restricted point. This means that the function must approach the same value from the left and right side of the restricted point, regardless of any limitations or restrictions on the function.
Yes, a limit can exist at a restricted point as long as the function approaches the same value from both sides of the restricted point.
To find the limit of a function with multiple restrictions, you must first determine if the function approaches the same value from both sides of each restricted point. If it does, then the limit at that point is the same value. If not, the limit does not exist at that point.
Yes, there are some special rules and techniques for finding limits with restrictions. These include using the squeeze theorem, L'Hopital's rule, and algebraic manipulation to simplify the function before taking the limit. It is also important to pay attention to any removable discontinuities or holes in the graph of the function.