Answer:
To evaluate the limit of the given expression as x approaches 4, you can try direct substitution first. However, in this case, direct substitution will lead to an indeterminate form of 0/0, so we'll need to simplify the expression first before evaluating the limit.
Start by factoring the expression and canceling out common factors:
lim(x→4) [(x - 4) / (20 - x) - 4]
Now, let's simplify further:
= lim(x→4) [(x - 4) / -(x - 20) - 4]
Notice that we have a common factor of -1 in the denominator:
= lim(x→4) [-1 * (x - 4) / (x - 20) - 4]
Now, we can factor out the -1:
= -lim(x→4) [(x - 4) / (x - 20) + 4]
Next, apply direct substitution:
= -[(4 - 4) / (4 - 20) + 4]
Now, evaluate the expression:
= -[0 / (-16) + 4]
= -[0 / -16 + 4]
= -[0 + 4]
= -4
So, the limit of the given expression as x approaches 4 is -4:
lim(x→4) [(x - 4) / (20 - x) - 4] = -4
Explanation: