For the following exercises, for each pair of functions, find a . ( f ∘ g ) ( x ) and b . ( g ∘ f ) ( x ) Simplify the results. Find the domain of each of the results. 44. f ( x ) = 2 x + 4 , g ( x ) = x 2 − 2
For the following exercises, for each pair of functions, find a . ( f ∘ g ) ( x ) and b . ( g ∘ f ) ( x ) Simplify the results. Find the domain of each of the results. 44. f ( x ) = 2 x + 4 , g ( x ) = x 2 − 2
For the following exercises, for each pair of functions, find
a
.
(
f
∘
g
)
(
x
)
and
b
.
(
g
∘
f
)
(
x
)
Simplify the results. Find the domain of each of the results.
Find the exact values of sin(2u), cos(2u), and tan(2u) given
2
COS u
where д < u < π.
2
(1) Let R be a field of real numbers and X=R³, X is a vector space over R, let
M={(a,b,c)/ a,b,cE R,a+b=3-c}, show that whether M is a hyperplane of X
or not (not by definition).
متکاری
Xn-XKE
11Xn-
Xmit
(2) Show that every converge sequence in a normed space is Cauchy sequence but
the converse need not to be true.
EK
2x7
(3) Write the definition of continuous map between two normed spaces and write
with prove the equivalent statement to definition.
(4) Let be a subset of a normed space X over a field F, show that A is bounded set iff
for any sequence in A and any sequence in F converge to zero the
sequence converge to zero in F.
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Establish the identity.
1 + cos u
1 - cos u
1 - cos u
1 + cos u
= 4 cot u csc u
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY