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2. (8 points) Let f(x)=beginarrayl 4,x<2 3x-22≤ x≤ 6 5x,x>6endarray. Find the indicated limits and function values. exist" or DNE if the value or limit does not exist. (a) limlimits _xto 2^-f(x)= _ (b) limlimits _xto 2^+f(x)= _ (c) limlimits _xto 6^-f(x)= _ (d) limlimits _xto 6^+f(x)= _ (e) f(2)= _ (f) f(6)= _ (g) Is ∫ continuous at x=2 7 _

2. (8 points) Let f(x)=beginarrayl 4,x<2 3x-22≤ x≤ 6 5x,x>6endarray. Find the indicated limits and function values. exist" or DNE if the value or limit does not exist. (a) limlimits _xto 2^-f(x)= _ (b) limlimits _xto 2^+f(x)= _ (c) limlimits _xto 6^-f(x)= _ (d) limlimits _xto 6^+f(x)= _ (e) f(2)= _ (f) f(6)= _ (g) Is ∫ continuous at x=2 7 _

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(a) 4 (b) 4 (c) 16 (d) 30 (e) 4 (f) 16 (g) continuous
1 Evaluate the limit from the left at x = 2 . Since f(x) = 4 for x < 2 , lim⁡x→2−f(x)=4 \lim\limits_{x \to 2^{-}} f(x) = 4
2 Evaluate the limit from the right at x = 2 . Since f(x) = 3x - 2 for 2≤x≤62 \leq x \leq 6 , lim⁡x→2+f(x)=3⋅2−2=4\lim\limits_{x \to 2^{+}} f(x) = 3 \cdot 2 - 2 = 4
3 Evaluate the limit from the left at x = 6 . Since f(x) = 3x - 2 for 2≤x≤62 \leq x \leq 6 , lim⁡x→6−f(x)=3⋅6−2=16\lim\limits_{x \to 6^{-}} f(x) = 3 \cdot 6 - 2 = 16
4 Evaluate the limit from the right at x = 6 . Since f(x) = 5x for x>6x > 6 , lim⁡x→6+f(x)=5⋅6=30\lim\limits_{x \to 6^{+}} f(x) = 5 \cdot 6 = 30
5 Evaluate f(2) using the function definition for 2≤x≤62 \leq x \leq 6 . f(2)=3⋅2−2=4f(2) = 3 \cdot 2 - 2 = 4
6 Evaluate f(6) using the function definition for x>6x > 6 . f(6)=5⋅6=30f(6) = 5 \cdot 6 = 30
7 Determine the continuity at x = 2 . Since lim⁡x→2−f(x)=lim⁡x→2+f(x)=4\lim\limits_{x \to 2^{-}} f(x) = \lim\limits_{x \to 2^{+}} f(x) = 4 and f(2) = 4 , f is continuous at x = 2
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