Final answer:
The infinite limit of lim x→4- x(x - 4)⁵ is 0 because as x approaches 4, the term (x - 4)⁵ approaches 0 and the whole expression ultimately approaches 0.
Step-by-step explanation:
To determine the infinite limit of lim x→4- x(x - 4)⁵, we first need to understand the behavior of the function as x approaches 4 from the left (denoted by '4-'). In this function, (x - 4)⁵ represents a fifth power which means as x approaches 4, this part of the function will approach 0. However, since x is being multiplied by this term, we must also consider the behavior of x as it approaches 4. Since x is approaching 4, x(x - 4)⁵ will ultimately approach 0 as all the terms are finite and the highest power of (x - 4) as x approaches 4 from the left is 0. Therefore, regardless of the higher power of (x - 4), the function will not approach infinity and instead, the limit is 0.