Final answer:
To solve the equation, factor the numerator and denominator and then cancel out the common factor. Evaluate the limit by plugging in the value of x. The final answer is -6.
Step-by-step explanation:
To solve the equation lim x--->4 (2-x)2 / (4-x), we can evaluate the limit as x approaches 4. Plugging in x=4 directly into the equation would result in division by zero, which is undefined. However, we can simplify the equation by factoring the numerator and denominator. After factoring, we can cancel out common factors and evaluate the limit.
By factoring, the equation becomes lim x--->4 (2-x)(2+x) / -(x-4)
Cancel out the common factor of (2-x) in the numerator and denominator. The equation now becomes lim x--->4 -(2+x) / -1. Evaluate the limit by plugging in x=4. The final answer is -6.