Consider the function f defined by f(x) its domain. a) First compute_lim f(x). Answer: x→∞ = and Q(x)? FORMATTING: 6+5e-3x 1-16e-3x b) Next we want to compute the limit in the opposite direction. As a goes to -∞, we get an indeterminate form of the type O 100 00⁰ 00x∞ 0/0 ○ ∞0/00 O∞-∞ Our goal in this question is to understand its behaviour as a goes to too, as well as near gaps in c) To be able to compute lim f(x), you have to rewrite f(x) as a fraction f(x) = x418 d) Using your answer in (c), compute lim f(x). Answer: x 8 Finally, we analyse f(x) near gaps in its domain. e) Find the point(s) a= a where f(a) is undefined. • Write your answer in the form [P(x), Q(x)], including the square brackets and comma. • Simplify so there are no fractional expressions in the numerator P(x) or denominator Q(x). • Strict calculator notation is required in your answer, meaning for multiplication (e.g. 3x is written 3*x, and e3x is written e^(3*x)). Answer: [P(x), Q(x)] = FORMATTING: List these points. If there are two or more such points, you must separate them by semi-colons (;). Since we are asking for exact values, your answers may involve the logarithm function In(). Answer: P(x) Q(x) f) For each of the values of \)a\) that you have found in (e), find the left-hand and right-hand limits of f as a approaches a. Then answer the questions below. For which point(s) a do we have lim f(x) = +∞o ? Answer: x→a that is no longer an indeterminate form. What are P(x) FORMATTING: If there are two or more points, separate them with semi-colons (). Since we are asking for exact values, your answers may involve the logarithmic function In()). You must use the notation of scientific calculators So 2x is written 2 * x, and so on. If there aren't any points, write empty. For which point(s) a do we have lim f(x) = -∞o ? Answer: x→a For which point(s) a do we have lim f(x) = +∞o ? Answer: x+a+ For which point(s) a do we have lim f(x) = -∞o ? Answer: x→a+ P a P ap