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16 - 4 11 +11 3. [8 points] Let f(1) == - where I > 0, 175 and f(5) = - mine if f is continuous at I=5. Explain. Deter-

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Beverley Smith
Beverley SmithLv2
10 May 2018
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(2+21=3 3 5. Let f(c)= -11 if : 71 Find all x where f() is continuous. if r=1 14 Solution: By the continuity theorems we have that f() is continuous for all 1 #1. For r = 1, we have = lim 11- -(x+3) = -4 11- 1 + 2.0 -3 : lim lim (+3)(x - 1) f(1) = 2-1 1-1 1-1- -(2-1) Thus, lim f(1) = f(1), so f(t) is not continuous at x = 1. Therefore, f(t) is continuous on (-0,1) U (1,0).

1. (a) Let f(x) = xe-* Find f'(x) and simplify your answer. [4 points) (b) Let y=zĀ® log2(x). Find dy and simplify. [4 points) [5 points) 8 - V163 , if 374 (c) For x > 0 let h(2) = 2 - k if x = 4 Find the value of the constant k that makes h continuous at x = 4.

2. (12 points) I 2? + 3.0 -1 if > 2 (a) Let f(x) = { Find all values of k such that f is k2.ā€“ 1-1 if I<2 continuous at r = 2. (b) Find the point(s) on the curve yĀ² +ry-r? = 9 where the tangent line is parallel to the line 2.0 + 4y +3=0.

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