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140Bquiz3csols

# 140Bquiz3csols - 4 To get the graph of h x =-5 x-1 start...

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1 MATH 140B QUIZ#3 Solutions Date: Sept 17, 2007 1. i) True . lim t 1 - C ( t ) = 0 . 1 and lim t 1 + C ( t ) = 0 . 2 ii) True . The left and right hand limits are different numbers. iii) False . The function C is discontinuous at t = 4. Therefore, C) is the answer. 2. First note: lim xto - 3 2 x 2 + 5 x - 3 x + 3 = lim xto - 3 (2 x - 1)( x + 3) x + 3 = lim xto - 3 (2 x - 1) = - 7 , i) True . The limit is - 7 , so left-hand-limit must be - 7 . ii) True . The limit is - 7 , so right-hand-limit must be - 7 . iii) False . It is a removable discontinuity not a jump (since the C -value does not jump on either side of t = - 3 . ) Therefore, D) is the answer. 3. i) True . lim x 0 3 x tan x = 3 lim x 0 x ( sin x cos x ) = 3 lim x 0 x sin x · cos x = 3 · 1 · 1 = 3 . ii) False . lim x 0 x csc( x/ 2) = lim x 0 x sin( x/ 2) = lim x 0 x/ 2 1 2 sin( x/ 2) = 2 lim x/ 2 0 x/ 2 sin( x/ 2) = 2 · 1 = 2 . where we mutliplied top and bottom by 1/2 at the 2nd equal sign. Therefore, A) is the answer.

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Unformatted text preview: 4. To get the graph of h ( x ) =-5 x-1 , start with the graph of y = 1 /x and shift it 1 unit to the right. Then re²ect the resulting graph in the x-axis 0.5 1.0 1.5 2.0 M 60 M 40 M 20 20 40 60 i) False . lim x → 1-h ( x ) = + ∞ . ii) True . lim x → 1 + h ( x ) =-∞ . iii) False . lim x → 1 h ( x ) = DNE . Therefore, B) is the answer. 2 5. From the graph below, all statements are easy to evaluate: 1 2 3 4 M 1.5 M 1.0 M 0.5 0.5 1.0 1.5 i) True . lim x → 2-g ( x ) =-1 . ii) True . lim x → 2 + g ( x ) = 1 . iii) True . The only discontinuity is at x = 2 . Therefore, E) is the answer....
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140Bquiz3csols - 4 To get the graph of h x =-5 x-1 start...

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