Final answer:
A reasonable estimate for the limit can be determined by evaluating the function at values close to 7. The best reasonable estimate for the limit among the given options is 7. The correct option is B.
Step-by-step explanation:
A reasonable estimate for the limit lim x→7 f(x) can be determined by evaluating the function at values close to 7. We can look at the values of the function as x gets closer to 7 from both sides to estimate the limit. Let's consider the options:
A) 4: If f(x) approaches 4 as x approaches 7 from both sides, then 4 is a reasonable estimate for the limit.
B) 7: The function value is exactly 7 at x=7, so this is a possible value for the limit.
C) 10: If f(x) approaches 10 as x approaches 7 from both sides, then 10 is a reasonable estimate for the limit.
D) 14: If f(x) approaches 14 as x approaches 7 from both sides, then 14 is a reasonable estimate for the limit.
Based on the given information, it is not possible to determine the exact value of the limit. However, the best reasonable estimate for the limit among the given options is B) 7.