Determine the following limits if it exists.
a. lim x-->5 (4x/x-5)
nope
4x/(x-5) -> 20/0
this is just algebra. Recall your rational functions work? Vertical asymptote at x=5.
Ik but shouldn't we try to factor the 4x. And I'm doing calc not adv fun anymore
To determine the limit of the given function as x approaches 5, you can substitute x = 5 into the expression and evaluate it. However, if you directly substitute x = 5, you will get an undefined value because of the division by zero in the denominator.
To overcome this, you can simplify the expression and try to cancel out the common factor causing the division by zero.
Let's simplify the expression:
f(x) = (4x / (x - 5))
To simplify further, you can factor out the common factor:
f(x) = (4x / (x - 5)) = (4x / (1(x - 5))) = (4(x / (x - 5)))
Now, you can see that (x - 5) is the common factor. As x approaches 5, this factor approaches 0.
Therefore:
lim x-->5 (4x / (x - 5)) = lim x-->5 (4(x / (x - 5)))
Now, you can substitute x = 5 into the expression:
lim x-->5 (4(x / (x - 5))) = 4(5 / (5 - 5))
However, here you still have division by zero. This indicates that the limit does not exist in this case because the function has a vertical asymptote at x = 5, resulting in an undefined value.
Hence, the limit does not exist for this function as x approaches 5.