Final Prep 3
Math 201
ame_
Construct a Frequenc Polygon (1 point) and then give the probability distribution (1 point) and sketch the
histogram for that distribution (1 point). Use 2 decimal places for your probabilities.
1) A class of 44 students took a
Week 4
Confidence Intervals and Chi Square (Chs 11 - 12)
For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significa
For full credit, you need to also show the statistical outcomes - either the Exc
1. Find all the fourth roots of -8 + 8iV3F. Express these in both polar and rectangular form. [10]
2. Prove: A function continuous on (a, b] attaim a minimum value on [8, b]- [10]
(Your proof should NOT involve sequences or compact sets!)
3. If (a, b) ~ (
Let f : U Rn > Rn be differentiable and U an open set in Rn , Suppose |f(x)| = 1 for all x in U Where
|f(x)| denotes the Euclidean norm of f(x) Show that f(x)t Df(x) = 0. Give a geometric interpretation of
this condition
Math 1B, Practice material for the First Midterm Examination Practice exam 1 1.(15 points) Evaluate the integral ( x2 ) dx x+1
2.(20 pnts) Evaluate the integral 1+x dx 1x
1
3.(25 pnts) Determine whether each improper integral is convergent or divergent. E
Practice Midterm Exam #3 1. Find the partial fraction decomposition of the function x+1 . x2(x2 + 1) 2. Evaluate x3 e x dx. 3. Determine whether the integral is convergent or divergent. Evaluate it if it is convergent.
e
1
dx . x(ln x)2
4. Evaluate the i
Practice Midterm Exam #2 1. Evaluate the integral x2 dx. (x + 1)3
2. Evaluate the integral
x dx. 1+x+ x
3. Determine whether each of the improper integrals is convergent or divergent. Evaluate the integrals which are convergent
1
(a)
1
x+1 dx. 3 x4 x2 x
Solutions to Practice Midterm #1 x1/3 ln x dx = 3 3 4/3 x = x4/3 ln x 4 4 3 4/3 9 x1/3dx = x ln x x4/3 + C ; 4 16 ln xd 2 3 u3 u1 3 4/3 x d ln x 4
1. (a)
3 3 = x4/3 ln x 4 4 (b) (c)
u+3 du = (u 1)(u 3)
du = 3 ln|u 3| 2 ln|u 1| + c;
dx (1 sin x) (1 sin x)
Practice Midterm Exam #1 Below is a sample of midterm which you can use for preparation. 1. Evaluate the following integrals: (a) (b) (c) (d) x1/3 ln x dx. u+3 du. (u 1)(u 3) dx . (1 + sin x) (1 + 1/2 x) dx.
2. Determine whether each improper integral is
Solutions to Practice Final 1B dt t = tan1 (x), dx = x = tan t, cos2 t
1. =
cos2 (tan1 (x)dx = cos2 t dt = cos2 t
1 n
dt = t + C = tan1 (x) + C
1 2. an = n
tan1 (n) + 1 1+
1 n3 1 n
, tan1 (n) + 1 1+
1 n3
1 lim an = lim lim n n n n 1 lim = 0, lim n n n
1 n
Math 1B, Final Examination N.Reshetikhin, May 13, 2005 P roblem P oints Grade 1 2 3 4 5 6 7 8 9 10 11 12 T otal 10 15 15 15 15 15 15 15 15 10 15 20 175
Students Name: GSIs name: Students i.d. number:
1.(10 pnts) Evaluate the integral e
x
dx
1
2.(15 pnts)
Math 1B, Final Examination N.Reshetikhin, May 18, 2004 Students Name: TAs name: Students i.d. number: 1.10 pnts Evaluate the integral x3 ex dx
2
1
2.15 pnts Evaluate the integral (t2 1 dx 1)(t 1)
2
3.15 pnts Indicate which of the following statements are
MAT 655: PreLab #11
Topic: Transformation Geometry
Instructions. This reading assignment is to be completed outside of class and before we cover
Lab #11 in class. You are expected to read and understand the material below. You are also
expected to submit