calculus midterm solutions

# calculus midterm solutions - Version 053 – Exam 1 –...

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Unformatted text preview: Version 053 – Exam 1 – Schultz – (56395) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Below is the graph of a function f . 2 4 6 − 2 − 4 − 6 2 4 6 8 − 2 − 4 Use the graph to determine lim x → 4 f ( x ) . 1. limit = 6 2. limit = 9 3. limit does not exist correct 4. limit = 8 5. limit = 14 Explanation: From the graph it is clear the f has a left hand limit at x = 4 which is equal to 9; and a right hand limit which is equal to 8. Since the two numbers do not coincide, the limit does not exist . 002 10.0 points When f is the function defined by f ( x ) = braceleftbigg 3 x − 7 , x ≤ 3 , 2 x − 5 , x > 3 , determine if lim x → 3+ f ( x ) exists, and if it does, find its value. 1. limit = 1 correct 2. limit = 0 3. limit does not exist 4. limit = − 1 5. limit = − 2 6. limit = 2 Explanation: The right hand limit lim x → 3+ f ( x ) depends only on the values of f for x > 2. Thus lim x → 3+ f ( x ) = lim x → 3+ 2 x − 5 . Consequently, limit = 2 × 3 − 5 = 1 . 003 10.0 points Determine lim x → 8 √ x + 1 − 3 x − 8 . 1. limit doesn’t exist 2. limit = 3 3. limit = 1 6 correct 4. limit = 6 5. limit = 1 3 Version 053 – Exam 1 – Schultz – (56395) 2 Explanation: After rationalizing the numerator we see that √ x + 1 − 3 = ( x + 1) − 9 √ x + 1 + 3 = x − 8 √ x + 1 + 3 . Thus √ x + 1 − 3 x − 8 = 1 √ x + 1 + 3 for all x negationslash = 8. Consequently, limit = lim x → 8 1 √ x + 1 + 3 = 1 6 . 004 10.0 points Determine lim h → f (1 + h ) − f (1) h when f ( x ) = 5 x 2 + 2 x + 5 . 1. limit does not exist 2. limit = 11 3. limit = 9 4. limit = 12 correct 5. limit = 13 6. limit = 10 Explanation: Since f (1 + h ) − f (1) = 5(1 + h ) 2 + 2(1 + h ) + 5 − 12 = 12 h + 5 h 2 = h (12 + 5 h ) , we see that lim h → f (1 + h ) − f (1) h = lim h → h (12 + 5 h ) h . Consequently, limit = 12 . 005 10.0 points Determine if the limit lim x → sin 5 x 6 x exists, and if it does, find its value. 1. limit = 6 2. limit doesn’t exist 3. limit = 5 6 correct 4. limit = 5 5. limit = 6 5 Explanation: Using the known limit: lim x → sin ax x = a , we see that lim x → sin 5 x 6 x = 5 6 . 006 10.0 points After t seconds the displacement, s ( t ), of a particle moving rightwards along the x-axis is given (in feet) by s ( t ) = 8 t 2 − 8 t + 3 ....
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## This note was uploaded on 09/06/2010 for the course M 32795 taught by Professor Schultz during the Spring '10 term at University of Texas.

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calculus midterm solutions - Version 053 – Exam 1 –...

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