All i need to know is what my limit is at x=1 or if the limit even exists.axmls said:You're correct, but perhaps you should go back and read about what it means for a limit to equal a value. Does it matter what happens to the function at the point you're approaching?
Which you will learn if you follow axmls's suggestion.AllanW said:All i need to know is what my limit is at x=1 or if the limit even exists.
The way things work here at PF is that we help you arrive at an answer, but we won't just give it to you.axmls said:perhaps you should go back and read about what it means for a limit to equal a value. Does it matter what happens to the function at the point you're approaching?
Okay, would i be correct if i said the limit for x at 1 would be -2?Mark44 said:Which you will learn if you follow axmls's suggestion.
The way things work here at PF is that we help you arrive at an answer, but we won't just give it to you.
Yes. Do you understand why?AllanW said:Okay, would i be correct if i said the limit for x at 1 would be -2?
I believe it because the limits approaching 1 from the left and right side is -2, what i don't understand is if and where the 'f(x)=3 when x=1' comes into playMark44 said:Yes. Do you understand why?
What does your book have for the definition of the limit of a function at some number?AllanW said:I believe it because the limits approaching 1 from the left and right side is -2, what i don't understand is if and where the 'f(x)=3 when x=1' comes into play
A piecewise function is a function that is defined by different equations over different intervals of the input variable. This means that the function has different rules for different parts of its domain.
To find the limits of a piecewise function, you need to evaluate the limits of each piece of the function separately. Then, you can compare the limits to see if they approach the same value. If they do, then that value is the limit of the entire piecewise function.
The most common methods for finding limits of a piecewise function are: using direct substitution, factoring and simplifying, and using the Squeeze Theorem.
Yes, a piecewise function can have an infinite limit. This can happen if one of the pieces of the function has an infinite limit or if the limits of the pieces approach different values from each side of the point.
A piecewise function is continuous if the function is defined at every point in its domain and if the limits from both sides of each point in the domain are equal. This means that there are no gaps or jumps in the graph of the function.