# HW 5 Calc - garcia (jjg2564) Hw 04 gualdani (56410) 1 This...

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: garcia (jjg2564) Hw 04 gualdani (56410) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine which of the following could be the graph of f near the origin when f ( x ) = x 2 7 x + 10 2 x , x negationslash = 2 , 4 , x = 2 . 1. 2. 3. 4. correct 5. 6. Explanation: Since x 2 7 x + 10 2 x = ( x 2)( x + 5) 2 x = 5 x , for x negationslash = 2, we see that f is linear on ( , 2) uniondisplay (2 , ) , while lim x 2 f ( x ) = 3 negationslash = f (2) . Thus the graph of f will be a straight line of slope 1, having a hole at x = 2. This eliminates four of the possible graphs. But the two remaining graphs are the same except that in one f (2) &gt; lim x 2 f ( x ) , garcia (jjg2564) Hw 04 gualdani (56410) 2 while in the other f (2) &lt; lim x 2 f ( x ) . Consequently, must be the graph of f near the origin. 002 10.0 points Find all values of x at which the function f defined by f ( x ) = x 5 x 2 5 x + 6 is continuous, expressing your answer in in- terval notation. 1. ( , 2) (2 , 3) (3 , ) correct 2. ( , 2) ( 2 , 3) (3 , ) 3. ( , 2) (2 , ) 4. ( , 3) (3 , ) 5. ( , 3) ( 3 , 2) ( 2 , ) Explanation: After factorization the denominator be- comes x 2 5 x + 6 = ( x 2)( x 3) , so f can be written as f ( x ) = x 5 ( x 2)( x 3) . Being a rational function, it will be contin- uous everywhere except at the zeros of the denominator since it will not be defined at such points. Thus f is continuous everywhere except at x = 2 and x = 3. Hence it will continuous on ( , 2) (2 , 3) (3 , ) . 003 10.0 points Determine which (if any) of the following functions is not continuous at x = 5. 1. f ( x ) = 1 | x 3 | x 5 1 2 x &lt; 5 2. all continuous at x = 5 3. f ( x ) = 1 x 3 x 5 1 2 x &lt; 5 4. f ( x ) = braceleftBigg 20 2 x 5 x negationslash = 5 4 x = 5 5. f ( x ) = braceleftbigg | x 5 | x negationslash = 5 x = 5 6. f ( x ) = braceleftBigg 1 x 5 x negationslash = 5 5 x = 5 correct Explanation: A function f will be continuous at x = 5 when f (5) exists and lim x 5 f ( x ) = f (5) . Now f (5) exists for all the functions defined above; in addition, inspection shows that all these functions have the property lim x 5 f ( x ) = f (5) except for f ( x ) = braceleftBigg 1 x 5 x negationslash = 5 5 x = 5 . . garcia (jjg2564) Hw 04 gualdani (56410) 3 Consequently, this function is the only one that is not continuous at x = 5....
View Full Document

## HW 5 Calc - garcia (jjg2564) Hw 04 gualdani (56410) 1 This...

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

View Full Document
Ask a homework question - tutors are online