We want to compute the limit below. To this end, we will use L'Hospital's Rule twice! lim sin(8x) 8x a) What is the indeterminate type of the limit? 0 00 - 00 0 : 00 b) Before we can use I'Hospital's Rule, we have to rewrite the limit as a fraction : lim lim A(z) x-+0 sin(8x) 8x x-+0 B(x) where [A(x), B(x)] = FORMATTING: Type your answer in the form [A(x), B(x)], include the square brackets and write a comma between A(x) and B(x). For this question, you must use strict scientific calculator notation, with * for multiplication (e.g. 3 sin(3x) is written "3*sin(3*x)"). c) Verify that lim A(2) x-+0 B(x) is an indeterminate form to which I'Hospital's Rule applies, and then apply I'Hospital's Rule to get lim A(z) = lim Al (z) c-+0 B(x) 2-+0 B1(x) where [A1 (x), B1(x)] = FORMATTING: Type your answer in the form [A1 (x), B1(x)], include the square brackets and write a comma between A1 (x) and B1(x). For this question, you must use strict scientific calculator notation, with * for multiplication (e.g. 3 sin(3x) is written "3*sin(3*x)"). d) Verify that lim A1 (2) x-+0 B1(x) is again an indeterminate form to which I'Hospital's Rule applies, and then apply I'Hospital's Rule to get Al (x) A2 (z) lim lim -0 B1(x) x-+0 B2(x) where [A2 (x), B2(x)] = FORMATTING: Type your answer in the form [A2 (x), B2 ()], include the square brackets and write a comma between A2 (x) and B2(x) . For this question, you must use strict scientific calculator notation, with * for multiplication (e.g. 3 sin(3x) is written "3*sin(3*x)"). e) Verify that lim A2 (x) 2-+0 B2(x) is no longer an indeterminate form, and conclude that A2 (a) lim sin(8x) 8x lim r-+0 B2(x)