Quest HW 4-solutions

# Quest HW 4-solutions - syed(sms3768 – Quest HW 4 –...

This preview shows pages 1–3. Sign up to view the full content.

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: syed (sms3768) – Quest HW 4 – seckin – (56425) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points What is the significance of the expression f (1 + h ) − f (1) h in the following graph of f when h = 9 2 ? 1 2 3 4 5 1 2 3 4 5 P Q R S T U 1. slope of tangent line at P 2. length of line segment PU 3. equation of line through P and T 4. slope of line through P and U correct 5. equation of line through P and R 6. length of line segment PR 7. slope of line through P and T 8. length of line segment PT 9. slope of line through P and R 10. equation of line through P and U Explanation: When h = 9 2 the expression f (1 + h ) − f (1) h is the ratio of the rise and the run between the points P and U . Thus the expression is the slope of line through P and U . 002 10.0 points If f is a differentiable function, then f ′ ( a ) is given by which of the following? I. lim h → f ( a + h ) − f ( a ) h II. lim x → a f ( x ) − f ( a ) x − a III. lim x → a f ( x + h ) − f ( x ) h 1. II only 2. I and III only 3. I only 4. I, II, and III 5. I and II only correct Explanation: Both of f ′ ( a ) = lim h → f ( a + h ) − f ( a ) h and f ′ ( a ) = lim x → a f ( x ) − f ( a ) x − a are valid definitions of f ′ ( a ). By contrast, lim x → a f ( x + h ) − f ( x ) h = f ( a + h ) − f ( a ) h because f is continuous. Consequently, f ′ ( a ) is given only by I and II . 003 10.0 points syed (sms3768) – Quest HW 4 – seckin – (56425) 2 Let f be a function such that lim h → f (1 + h ) = 2 , and lim h → f (1 + h ) − f (1) h = 3 . Which of the following statements are true? A. f is continuous at x = 1 , B. f (1) = 3 , f ′ (1) = 2 , C. f is differentiable at x = 1 . 1. A only 2. A and C only correct 3. B only 4. C only 5. A and B only 6. all are true 7. none are true 8. B and C only Explanation: A. True: f is differentiable at x = 1, so also continuous at x = 1. B. False: by definition, f is differentiable at x = 1 and f ′ (1) = 3. C. True: by definition. 004 10.0 points Let f be the function defined by f ( x ) = 7 x − ( x − 3 + | x − 3 | ) 2 . Determine if lim h → f (1 + h ) − f (1) h exists, and if it does, find its value. 1. limit = 5 2. limit = 8 3. limit = 9 4. limit doesn’t exist 5. limit = 6 6. limit = 7 correct Explanation: Since f ( x ) = braceleftbigg 7 x, x < 3, 7 x − 4( x − 3) 2 , x ≥ 3, we see that lim h → f (1 + h ) − f (1) h = f ′ (1) because 1 , 1 + h < 3 for all small h . Conse- quently, limit = 7 ....
View Full Document

## This note was uploaded on 04/29/2010 for the course MATH 408K taught by Professor Seckin during the Spring '10 term at University of Texas-Tyler.

### Page1 / 9

Quest HW 4-solutions - syed(sms3768 – Quest HW 4 –...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online