Math 1B: Calculus
February 10, 2010
Quiz 3
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers 1. (2 pts) Evaluate 4x2 1 dx. x
This requires a trigonometric substitution, and since 4x2 1 = (2x)2 1 we may choose 2x = sec , 2 dx = sec tan d: 4x2 1 s
Homework 4 for statistics
1. Number of groups k = 3
Number of data points = 3*20 = 60
Degree of freedom for treatment = k 1 = 3 1 = 2
Degree of freedom for error = n k = 60 3 = 57
F critical for 0.05 level of significance = 3.1588
Number of groups k = 3
N
Math 1B: Calculus
February 3, 2010
Quiz 2
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers 1. (2 pts) Evaluate dx . x2 x2 4 We have the expression x2 a2 in the integrand, with a = 2, so we make the substitution x = a sec = 2 sec , dx = 2 sec ta
Dylan Aronson William Berry ENV SCI 24 12/02/09 Sustainability Sustainability, in its broad sense, is the ability for something to be maintained at a certain rate or level. Therefore, when discussing sustainability in the context of life on earth, it is d
Math 1B: Calculus
February 3, 2010
Quiz 2
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers 1. (2 pts) Evaluate dx . (4 x2)3/2 We have the expression a2 x2 in the integrand (even if cubed), with a = 2, so we make the substitution x = a sin = 2 s
Math 1B: Calculus
March 3, 2010
Quiz 5
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers 1. (2 pts) Is
n=2
1 convergent or divergent? Justify your answer. n ln n
Since x and ln x are increasing functions of x, it follows that x1 x is a decreasi
Math 1B: Calculus
March 3, 2010
Quiz 5
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers
1. (2 pts) Is
n=2
1 convergent or divergent? Justify your answer. n(ln n)2
1 Since x and ln x are increasing functions of x, it follows that x(ln x)2 is a d
Math 1B: Calculus
February 24, 2010
Quiz 4
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers Determine whether the following sequences converge or diverge. If they converge, nd the corresponding limit. (Justify your answer.) 1. (2 pts) an = log
Math 1B: Calculus
February 24, 2010
Quiz 4
Lecturer: Prof. Mina Aganagic GSI: Gary Sivek
Name: Answers Determine whether the following sequences converge or diverge. If they converge, nd the corresponding limit. (Justify your answer.) 1. (2 pts) an = cos
Homework 2
1. Z-score defines the 0.05 critical region for one tailed test: 1.645
For left tailed test critical region is z < -1.645
For right tailed test critical region is z > 1.645
2. Z-score defines the 0.05 critical region for two tailed test: 1.96,