Question Detail
Question
lim x→3 (x5-243)/(x3-27) equal
Correct Answer
Option B is the correct answer.
Detailed Explanation
This limit is in the indeterminate form 0/0 when x=3 (since 35 = 243 and 33 = 27). We can use L'Hôpital's Rule or factorization.Using L'Hôpital's Rule:Differentiate the numerator and the denominator separately with respect to x:lim x→3 d/dx(x5-243)/d/dx(x3-27) = lim x→3 5x4/3x2Simplify the expression:lim x→3 5x2/3Now substitute x=3:5(3)2/3 = 5 * 9/3 = 5 * 3 = 15. This matches option B.
Hint
This is an indeterminate form 0/0. Consider applying L'Hôpital's Rule or factorizing the numerator and denominator using the difference of powers formula (an - bn = (a-b)(an-1 + ... + bn-1)).