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samptest-2-Fa07

# samptest-2-Fa07 - MATH 1501 Sample Quiz Questions for Test...

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Unformatted text preview: MATH 1501 Sample Quiz Questions for Test 2, Fall 2007 WTT Note 1: Just as was the case with sample problems for Test 1, there are more questions—by far— than you can expect on an hour exam. I am hoping this more comprehensive version will be of greater assistance to students in studying for the test. Also, I haven’t left as much space on the pages as will be the case on an actual hour test. 1. For what values of x is the function f ( x ) = sin 2 x +sin x concave upwards? Concave downwards? Find all inflection points. Find where it achieves local maxima and local minima. 2. Use differentials to approximate: • √ 36 . 7 • sin( . 02). • (27 . 15)- 2 / 3 . 3. Use the Newton-Raphson method to find x 1 , x 2 and x 3 when f ( x ) = x 2- 5 x + 6 and x = 4. To what value will this sequence converge? 4. Let f be a function that is continuous on an interval [ a,b ]. Define the Reiman integral: R b a f ( x ) dx : Answer Z b a f ( x ) dx = lim μ ( P ) → Σ n i =1 f ( t i )Δ( x i ) Note: You should also know this answer implicitly includes • P = [ x ,x 1 ,...,x n ] is a partition of [ a,b ]; • Δ( x i ) = x i- x i- 1 ; • for each i = 1 , 2 ,...,n , the number t i belongs to the sub-interval [ x i- 1 ,x i ] ( Note. The textbook uses the notation x * i rather than t i ); and • μ ( P ), the mesh of P , is max { Δ( x i ) : 1 ≤ i ≤} . 5. State the First Fundamental Theorem: Answer Let f and G be continuous on [ a,b ] with G differentiable on ( a,b ). If G ( x ) = f ( x ) for all x from ( a,b ), then Z b a f (...
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samptest-2-Fa07 - MATH 1501 Sample Quiz Questions for Test...

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