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13 Dec 2017

5. If f(x)= 27° -5x + 3x –7 then A) lim f(n= f(x)=0 B) lim f(x)=0 D) lim f(x)=-- C) lim E) None of these

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Nestor Rutherford
Nestor RutherfordLv2
15 Dec 2017
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Joey Tang
Joey Tang
Bachelor’s Degree in Chemistry from McMaster University
20 May 2020

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In(e*-*) if x 23 A) lim f (x) doesn't exist B) lim f(x)=0 C) lim f(x)=6 D) limf(x)= 3 E) lim f(x)=-3

5. (18 pts) Circle True if the statement is ALWAYS true; circle False otherwise. No explanations are required. Let f be a one-to-one function and f its inverse. (a) If the point (2, 5) lies on the graph off, then the point (5,2) lies on the graph of f. True False f (2) = 5 f-1 (5) = 2 (b) sin-1 (T) = 0 True False Since >1, ris not in the domain of sin-?; | or sin-1 (7) #0, since sin (0) = 0 # Iff and g are two functions defined on (-1, 1), and if (c) limg (x) = 0, then it must be true that lim[ f(x) g (x)] = 0. True False Let f (x) = 1 / x, if x #0, and f (0) = 4 and g(x) = x. Then lim g (x) = lim (x) = 0, but Lim ( f (x) g(x)] = lim [() x] = 18 0. Iffis continuous on (-1, 1), and if f (0) = 10 and lim g (x) = 2, (a) True False then lin (= 5. Because lim : (*) - Limx-of (*) .f(0) = 20 = 5 If f is continuous on [1, 3], and if f(1) = 0 and f(3) = 4, then the equation f(x) = (e) has a solution in (1, 3). True False Since f continuous on [1, 3), f(1) = 0 < < 4 = f (3), by the Intermidiate Value Theorem there exists a cin (1, 3) such that f (c) = . (f) Let f be a positive function with vertical asymptote x = 5. Then lim f (x) = +0. True False Let f (x) = 1, if x < 5, and f (x) ==, ifx>5. Then lim f (x) = +00, and therefore, X = 5 is a vertical asymptote. 5 - X So, f is a positive function with vertical asymptote x = 5 but lim f (x) + +co, since lim f (x) = + 0 + lim f (x) = 1, which means that lim f (x) does not exist.

2. a) Sketch the graph of a function f(x) that satisfies all the below conditions: 1- 0 1+0+ i) lim f() = 2 and lim f(0) = -1 and f(0) = -1 ii) lim f(x) = 3 and f(x) is discontinuous at x = 2 iii) lim f(x) = 0 and f(-3) = 2 2 +2 y=f(x) (7 marks) + N

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