In the following exercises, use the graph of the function to find the indicated values. 383. (a) Find: f ( 0 ) . (b) Find: f ( 1 2 π ) . (c) Find: f ( − 3 2 π ) . (d) Find the values for xwhen f ( x ) = 0 . (e) Find the x -intercepts. (f) Find the y -intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.
In the following exercises, use the graph of the function to find the indicated values. 383. (a) Find: f ( 0 ) . (b) Find: f ( 1 2 π ) . (c) Find: f ( − 3 2 π ) . (d) Find the values for xwhen f ( x ) = 0 . (e) Find the x -intercepts. (f) Find the y -intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.
Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045.
2) Find Θ given sec Θ = 4.213.
3) Find Θ given cot Θ = 0.579. Solve the following three right triangles.
B
21.0
34.6° ca
52.5
4)c
26°
5)
A
b
6) B 84.0 a
42°
b
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
Elementary Statistics: Picturing the World (7th Edition)
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