Explain in your own words what is meant by the equation `lim_(x->2) f(x) = 5` Is it possible for this statement to be true and yet `f(2) = 3`? Explain
In words, this equations says "the limit of the function 'f of x', as x approaches the value 2, is equal to the value 5". This means that as we choose values of x less than and greater than 2, the value of the function f(x) approaches 5 from the left and from the right. But the function could have a 'hole' at x = 2, and have the point value f(2) = 3. Please see the attached example.
The equation `lim_(x->2) f(x) = 5` means that for the values of x approaching to 2, the values of the function f (x) are being 5. As we go the closer to the x values of 2, the closer the resulting f (x) values are supposed to get to 5.
Yes,It is possible for the limit to equal 5 even though f (2) = 3. The function` f (x) = [[(1 - x^2)]]` , the limit as x approaches 0 is 0, but f (0) = 1. so now we can create a relation as the function
`f (x) = 5- 2 [[(1- (x-2)^2)]]`
and for this function, the limit as x approaches 2 is 5, but f (2) = 3