Knowing that lim 1 = 0 for a > 0, we want to evaluate the following limit. 1481 lim *400 a) This is an indeterminate form of the type 0 - 0 0/0 0 100 000/00 0.0 0.0x0 b) Rationalize this expression to find polynomials p(x), g(x) and r(a) such that +62- ( +62-2-32) p(x) q(2) + r(2) FORMATTING: Write your answer in the form [p(z), g(1), r(z)), including square brackets and commas between the terms. Use strict scientific calculator notation in your answer, in particular for multiplication (e.g. 32 is written 3*x^2, and 2(3x + 1) is written 2*(3*x+1)). Note that you should not have sqrt() in your answer. Answer: [p(a), g(z), r(z)] = () d) Use your work above to compute lim 200 Answer: c) Simplify the expression from part (b) so that the numerator is a constant. Use the fact that=1 and present your answer in the form 9(2) + r(2) 8(T) + (2) where C' is a constant and s(a) and t(z) don't diverge to oo as a increases. FORMATTING: Write your answer in the form [C, s(x), t(x)], including square brackets and commas between the terms. Use strict scientific calculator notation in your answer, in particular for multiplication (e.g. 3x2 is written 3*x^2, and 2(3x + 1) is written 2*(3*x+1)). Note that you should not have sqrt in your answer. Answer: [C, s(x), t(x)] = + 6 - - 3x = 3z