Final answer:
The value of the limit as h approaches 0 for the expression (8h)^13 - 2h/h is -2. Upon evaluating the limit, the term involving h raised to the power of 13 approaches zero, and thus the result simplifies to just -2. The correct answer is -2.
Step-by-step explanation:
To find the value of lim h→0(8h)¹³-2h/h, we need to apply limits. As h approaches zero, the term 8h¹³ becomes insignificant because any non-zero number raised to a positive power will approach zero as the base approaches zero. Thus, this term can be treated as zero in the limit. On the other hand, the term -2h/h simply reduces to -2, as the h in the numerator and denominator cancel each other out. Therefore, the limit simplifies to:
lim h→0(8h)¹³-2h/h = lim h→0(0)-2 = -2
However, if we analyze the initial expression (without considering the exponentiation), we notice that there's a common factor of h in the numerator, which means the expression actually simplifies to 0 upon dividing by h in the denominator before taking the limit. Therefore, the correct calculation is as follows:
lim h→0(8h¹³-2) = (lim h→0 8h¹³) - (lim h→0 2) = 0 - 2 = -2.
Thus, the answer to the question is B) -2.