For each function in Problems 19-22, approximate f '(a) in the following ways. Use f ( a + h ) − f ( a ) h with h = 0.0001. (b) Graph the function on a graphing calculator. Then zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. f ' ( 2 ) for f ( x ) = 3 x 4 − 7 x − 5
For each function in Problems 19-22, approximate f '(a) in the following ways. Use f ( a + h ) − f ( a ) h with h = 0.0001. (b) Graph the function on a graphing calculator. Then zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. f ' ( 2 ) for f ( x ) = 3 x 4 − 7 x − 5
For each function in Problems 19-22, approximate f'(a) in the following ways.
Use
f
(
a
+
h
)
−
f
(
a
)
h
with
h
=
0.0001.
(b) Graph the function on a graphing calculator. Then zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see.
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.
އ
Establish the identity.
1 + cos u
1 - cos u
1 - cos u
1 + cos u
= 4 cot u csc u
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