HW08-solutions

# HW08-solutions - husain(aih243 – HW08 – Gilbert...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: husain (aih243) – HW08 – Gilbert – (56215) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A certain function f is given by the graph 4 8 − 4 − 8 4 − 4 − 8 (i) What is the value of lim x →−∞ f ( x ) 1. limit = − 1 2. limit = 2 3. limit = 1 4. limit does not exist 5. limit = − 2 correct Explanation: To the left of x = − 2 the graph of f os- cillates about the line y = − 2 and as x ap- proaches −∞ the oscillations become smaller and smaller. Thus limit = − 2 . 002 (part 2 of 3) 10.0 points (ii) What is the value of lim x →∞ f ( x )? 1. limit does not exist 2. limit = 1 correct 3. limit = − 1 4. limit = − 2 5. limit = 2 Explanation: To the right of x = 1 the graph of f is asymptotic to the line y = 1. Thus limit = 1 . 003 (part 3 of 3) 10.0 points (iii) What is the value of lim x →− 2 f ( x )? 1. limit = 1 2. limit = 2 3. limit = ∞ correct 4. limit = − 1 5. limit = − 2 Explanation: From the graph of f the left hand limit lim x →− 2 − f ( x ) = ∞ , while the right hand limit lim x →− 2+ f ( x ) = ∞ . Thus the two-sided limit lim x →− 2 f ( x ) = ∞ . 004 10.0 points husain (aih243) – HW08 – Gilbert – (56215) 2 Determine if the limit lim x →∞ 3 x + 1 x 2 − x + 5 exists, and if it does, find its value. 1. limit = 1 5 2. limit = 0 correct 3. limit doesn’t exist 4. limit = 1 5. limit = 5 6. limit = − 3 Explanation: Dividing in the numerator and denominator by x 2 , the highest power, we see that 3 x + 1 x 2 − x + 5 = 3 x + 1 x 2 1 − 1 x + 5 x 2 . On the other hand, lim x →∞ 1 x = lim x →∞ 1 x 2 = 0 . By Properties of limits, therefore, the limit exists and limit = 0 . 005 10.0 points Determine if the limit lim x →−∞ √ x 2 + 5 x 5 x + 3 exists, and if it does, find its value. 1. limit does not exist 2. limit = 5 3 3. limit = 1 4. limit = − 1 5 correct 5. limit = − 5 3 6. limit = − 1 7. limit = 1 5 Explanation: Since √ x 2 = | x | , ( √ a is always non- negative, remember), the given expression can be written as √ x 2 + 5 x 5 x + 3 = | x | x parenleftBig radicalbig 1 + 5 /x 5 + 3 /x parenrightBig . But lim x →−∞ radicalbigg 1 + 5 x = 1 , lim x →−∞ parenleftBig 5+ 3 x parenrightBig = 5 . On the other hand, lim x →−∞ | x | x = − 1 . Consequently, by Properties of Limits, the given limit exists, and limit = − 1 5 . 006 10.0 points Use intercepts and asymptotes to decide which of the following functions has husain (aih243) – HW08 – Gilbert – (56215) 3 as its graph. 1. f ( x ) = 3 − x x + 3 2. f ( x ) = x + 3 x − 3 3. f ( x ) = x − 3 x + 3 correct 4. f ( x ) = x + 3 x + 3 5. f ( x ) = x − 3 x − 3 Explanation: The graph of any function f ( x ) = ax − b x + c has the properties (i) a horizontal asymptote y = a , (ii) a vertical asymptote x = − c , (iii) an x-intercept at x = b a...
View Full Document

{[ snackBarMessage ]}

### Page1 / 13

HW08-solutions - husain(aih243 – HW08 – Gilbert...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online