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двадцать четвёртая буква английского алфавита: - прописная, - строчная
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1. squared
x
to the i?
2. -- -- has parametric equation
x
= - 3t, y = 3t,
3. Suppose I go out to
x
=2.
4. And we wrote out what
x
was.
5. partial f over partial
x
times partial
x
over partial v plus
6. change. Now, how quickly does
x
change?
7. partial g over partial
x
. We can just write g sub
x
times
8. gradient vector. So, here at
x
,
9. There's a random variable
X
and you're
10. what is it?--
x
to the d/2 minus 1 e to the minus
x
/2.
11. v over partial of
x
, y.
12. So we are going to rewrite that as f(
x
) is equal to
x
times (
x
+6) to the 1/2 power.
13. say,
x
to be the rate of change with respect to
x
when we hold
14. over 1 minus
x
.
15. Second derivative of
x
squared is?
16. the elements of this set capital
X
are n vectors so each element of capital
X
is
17. AUDIENCE: Multiply by
x
.
18. We know how
x
depends on z. And when we know how
x
depends
19. Solving A
x
--
20. And this term becomes
x
bar squared.
21. And this is just C times
x
.
22. R25007 Utility 4000D-
X
23. It's this quantity,
x
+iy.
24. and w_2 be minus its
x
derivative,
25.
x
, y, and z, right? These guys depend on
x
, y, z.
26.
x
- y^2.
27. and it has the property that IX equals
X
for all
X
.
28. The second
x
derivative, if the function is
x
, is zero.
29. Now when you write print
x
, if
x
is a float variable, Python
30.
x
-axis. The change of variables for
31. equals 1 minus
x
to the n plus 1 over 1 minus
x
minus 1,
32. parametric equation.
X
will start at - 1,
33. amount which is approximately f sub
x
times delta
x
plus f sub y
34. equals 1 minus
x
to the n over 1 minus
x
.
35. How do you figure u(
x
+h)?
36. is if
x
is less than y,
x
is greater than y,
37. formula, we will get that df is f sub
x
times
x
prime t dt plus
38. assume
X
is piecewise constant
39. basically. And, what's delta
x
?
40. For example,
x
is over here.
41. value of
x
, but
x
is positive in our origin.
42. then
x
is zero.
43. same it's also constant where
X
is constant or where there's a jump in
X
44. y variable is going to increase with
x
or decrease with
x
, I am just looking for is
45. So it might have
x
and y.
46. It just prints
x
and crashes.
47.
x
,y,z, that
x
,y,z themselves depend on
48. and closer to the solution,
x
. Is
x
a solution? Yeah, because y equals
x
is an integral curve.
49. switch to usual coordinates
x
and y.
50.
x
is good.
51. I'm looking at
x
squared.
52. point it jumps to one okay so this is what your
X
function your
X
curve looks
53. So that's just
x
. So, that means that du dv is
x
54. Remember 1 minus
x
.
55.
x
cubed is real.
56. mentalistic idioms of propositional attitude--
x
believes that p,
x
regrets that p,
x
hopes
57. to be y' = -
x
/ y.
58. A
x
-- that's very important.
59. think the answer will be
x
.
60. But what's the value of
x
?
61. If
x
was even,
x
divided by two is going to be actually
62. plus 1 over 1 minus
x
.
63. the direction field. Its slope at the point was to be
x
, whatever the value of
x
was,
64. unknown vector,
X
, equals some known vector,
65. Multiply by
x
, I get that
x
squared
66. we should change (
x
, y) to (-y,
x
).
67. will be roughly (u sub
x
times change in
x
) (u sub y times
68.
x
and y are less than epsilon.
69. C times
x
, right?
70.
X
parenthesis 1,
X
parenthesis 2, et cetera.
71. Where
x
and y are floats.
72. Let's say I give you the function f(
x
;y)=
x
^2 - 2xy 3y^2
73. PROFESSOR:
x
-range?
74. That would be (
x
- y)^2 2(
x
- y), and then there is a plus
75. value everywhere I see
x
.
76. square root of
x
.
77. positive values of
x
?
78. Does
x
change?
79. matrix |u sub
x
, u sub y, v sub
x
,
80. I'm going to say that the
x
part is really
x
times --
81. I have indexed
x
and y.
82. A times
x
.
83. I'll make that
x
--
84. partial
x
of the second component,
85. We get
x
is equal to 1.
86. what am I looking at?
x
squared.
87. be approximately u sub
x
delta
x
,
88.
x
and then there's a little correction
89. Fib of
x
- 1 and fib of
x
- 2, and then take the sum of those
90. that gives me a sequence of values,
x
,
x
plus 1
91. less linearly on
x
, y and z.
92. So that's C times
x
.
93. when we change
x
, y, z slightly,
94. the sqrt (C1 -
x
^2). We'll make the
x
squared because that's the way people usually put the radius.
95. and set
x
to zero.
96. for a particular
x
.
97. And this critical point, (
x
,y) = (-1;0),
98. parallel to the
x
, z plane.
99. changes in
x
, y, z,
100. square it is close enough to
x
.
101. It is going to be f sub
x
times
x
sub u times f sub y times y
102. AUDIENCE: What's
x
-range?
103. alright, so e^
x
transforming the plane
104. What's the real part of this
x
+iy squared?
x
squared,
105. to
x
, right?
106.
x
values. We are predicting y values from our response to
x
. So we have four checks
107. That's
x
times --
108. on 4D signals--
x
, y, z, time.
109. well, you want to take partial f over partial
x
times partial
x
110. over the square root of the summation of
x
minus the mean of
x
squared. The standard
111. A took
x
into b up there, and then A inverse brought back
x
.
112. 2200, partial h over partial
x
equals
113. while
x
is less than--
114. one, but with
x
and
x
plus delta
x
,
115. respect to
x
, take the
x
component,
116. times
x
giving a vector b.
117. I'm in three dimensions,
x
, y, z.
118. This
x
only gets seen by sqrt.
119. Right?
x
is initially bound to fifteen.
120. What's
x
?
121. The derivative of 1/2
x
, or
x
/2 is equal to 1/2.
122. Well, the rate of change of
x
in this situation is partial
x
,
123. So it's just adding 1 to
x
.
124. I'm starting with this
x
.
125. At
x
=0.
126. So, that really is included. How about the
x
-axis? Well, the
x
-axis is not included.
127. matrix |u sub
x
, u sub y, v sub
x
,
128. oh... y' =
x
/ y
129. f sub
x
equals lambda g sub
x
, f sub y equals lambda g sub y,
130. Because
x
squared would give me two
131. divided by (
x
+6)^-1/2.
132.
x
is equal to y.
133. be a1. That's partial w partial
x
.
134. actually depends on
x
and y and
x
and y depend on u.
135. over 4 cosine cubed of
x
/2.
136. IF
x
is less than z, and if that's true, print out
x
is
137. In general, the identity matrix in size n
x
n is an n
x
n matrix
138. an
x
problem, a shortest path problem.
139. and get back to
x
.
140. to be
x
squared minus
x
minus six is equal to zero. This one is very easily factored.
141.
X
plus
x
squared plus
x
cubed plus
x
142. Remember 1 minus
x
.
143. Now, what about this u(
x
-h)?
144. we're going to display
x
.
145. between
x
equals zero and one.
146. they are
x
^2 y^2, y^2 -
x
^2, they are sums or differences of
147. like
x
equals 3 plus 4.
148. Well, are
x
ad y still connected?
149. the value of
x
.
150. first. So, that was
x
equals zero.
151. is just 1 over 1 minus
x
.
152. partial derivative first with respect to
x
,
153. All I'm left with is
x
over 1 minus
x
squared.
154. Does
x
change?
155. variables,
x
, y, z and lambda.
156. The function
x
should come out right.
157. and lets integrate with respect to
x
.
158. or I have some
x
-ray vision.
159. partial derivatives. What is f sub
x
?
160. So what is
x
in polar coordinates?
161. and something that looks like integral of h of
x
p of
x
dx.
162. If I plug in
x
=1/6...
163. delta
x
and v sub
x
delta
x
. There's no delta y.
164. f sub
x
tells us what happens if we change
x
a little bit,
165. We have
x
space, not time.
166. If we change
x
by a certain amount delta
x
,
167. is the
x
value of -1.
168. got the value of
x
multipied by
x
, which of course is nine,
169. Plug in
x
=1/6?
170. derivatives, so partial f partial
x
and
171. f of
x
, dx.
172. A function g of
x
is tilde, a function h of
x
173. So -1/2
x
squared plus 1/2
x
.
174. over here -- equal f(
x
,y).
175. One minus
x
to the n.
176. Minus
x
squared.
177. PROFESSOR: This is a big
X
and this is a small
x
.
178. value,
x
. So, that's actually
x
- 2, right?
179. PROFESSOR: Multiply by
x
.
180. f(
x
)?
181. We need also
x
sub u,
x
sub v, y sub u,
182. Let's assume that
x
is a number.
183. variables,
x
, y, z,
184. that is
x
^2 y z. And let's say that maybe
x
will
185. Suppose that
x
is equal to 8.
186. Well, does u=
x
solve Laplace's equation?
187. We have secant
x
/2 times secant squared
x
/2 times 1/2... doing that derivative of that
188. equals 12 + 4 b
x
189. This equals 1 minus
x
to the n over 1 minus
x
minus the 1,
190. to abs of
x
plus 1.
191. between
x
and y and
X
of Z as I take Y super close to zero that's zero right
X
192. it bound
x
to the value three, and then it took
x
times
x
,
193. than equal to
x
.
194. This is mu sub
X
of r.
195. Take this side. This side in
x
,
196. negative y and
x
then this curl is going to be N sub
x
minus M
197. roughly (v sub
x
delta
x
) (v sub y delta y).
198. Let me suppose
x
is one, so I'll take
x
to be one.
199. f(
x
) is equal to
x
times the square root of
x
+6.
200. just to take another
x
.
201. changes. Well, f might change because
x
202. So this is going to be (
x
+3) times (
x
-1) is equal to zero.
203. no
x
would work.
204. My notes say
x
, but it's the wrong thing-- if f of
x
, f of
205. the half of
x
, right?
206. so
x
-Axis
207. difficulty. You just exchange roles of
x
208. Suppose I take u(
x
,y)=
x
.
209. Plug in
x
=1.
210. How do you do
x
+iy squared?
211. What is age
x
?
212. I'm binding
x
to the value three?
213. i times
x
to the i.
214. Well, are
x
ad y still connected?
215. And what about
x
?
x
is constant equal to x1 so dx
216. And therefore S equals 1 minus
x
to the n over 1 minus
x
.
217. different derivatives, partial f, partial
x
,
218.
x
is connected to y.
219. It still works, right? u(
x
) is still -1/2 of
x
squared.
220. So I have 1/2 secant
x
/2 times tangent
x
/2.
221. The derivative of
x
to the i is just i times
x
to the i
222. or
x
equals something.
223. Well, what's the slope of y1(
x
)? That's y1'(
x
). That's from the first day of 18.01, calculus.
224. so let's get started the proof we begin with an allocation
X
at the moment
X
225. Minus
x
to the n.
226. and that's approximately the derivative, u'(
x
).
227. Three times (
x
y) - (2x - z) will be
x
3y z.
228. So it's some
x
cubed.
229. To the value, not to
x
.
230. value of
x
is 8.
231. or
x
squared.
232. Because Of
X
, Why
X
? because of Z?
233. it draws, at (
x
, y), the little line element having slope f(
x
, y). In other words, it does
234. Equipotentials,
x
equal a constant.
235. What are
x
and y?
236. u(
x
+h) - u(
x
), just how much did that step go.
237. that this function normally depends on
x
.
238. what
x
do we actually get?
239. AUDIENCE: What's
x
-range?
240. Remember w was
x
^2y z.
x
was t, so you get t squared,
241. is really small, or
x
is really large or
x
is really small,
242. expression
x
times
x
.
243. And -
x
2y=3.
244. What about
x
squared?
245. if we move in the
x
, y coordinates by delta
x
and
246. of
x
, y, z when we change u. And now, when we change
x
,
247. line y equals
x
, not beyond that.
248. At
x
=0, that's obviously zero.
249. Whoops, I shouldn't have said
x
.
250. Two
x
minus y plus zero z.
251. I get (
x
- y)^2 2 (
x
- y) 1. But I will have minus one that
252. and v sub
x
delta
x
. And, on the other hand,
253. the whole
x
-axis. It's just a limited piece of the
x
-axis where that solution is defined.
254. in the
x
direction. Things make sense.
255. and a huge congratulation to mod
X
underscore of
X
X
for a winning the
256. Well, it's fd of
x
is--
257. I'm using the same c(
x
,y) in the
x
direction and the y
258. That's for
x
, exactly.
259. So it has
x
, y, and z.
260. plus
x
plus
x
squared plus
x
to the n minus 1,
261. It's 1 over 1 minus
x
.
262. When
x
is two, what is y?
263. So I keep switching from small
x
to large
X
. Everybody
264. is below the
x
axis.
265. IF
x
is y-- sorry, IF
x
is less than y, THEN check to see
266. get
x
plus
x
squared and so forth, up to
x
to the n,
267. well. How does
x
depend on u?
268. takes
X
and gives you
X
again. It's called I,
269. partial x's. Let's simplify by partial
x
.
270. relationship between y on
x
, or the regression line between y on
x
. Standard Error of Residuals
271. formulas. So, u equals
x
,
272. Transform from
x
to b.
273. We multiply the sum by
x
to get
x
plus
x
squared plus-- I've
274. minus
x
squared.
275. ix to the i equals
x
minus n plus 1,
x
to the n plus 1,
276. of
x
in, changes
x
to
x
+1, and then just returns the value.
277. partial
x
, well, what is that?
278. Namely
x
equals zero is a solution.
279. So now that u(
x
+h) - u(
x
-h) is zero,
280. sub u du plus f sub
x
,
x
sub v plus f sub y y sub v
281. the coordinates
x
, y, z,
282. Well, partial g over partial
x
times the rate of change of
x
.
283. that i equals 0 to n,
x
to the i equals 1 minus
x
to the n
284. I subtract u(
x
) - U(
x
-h) and I get two -u(
x
)'s This is what I
285. assignment statement,
x
now is a variable
286. at A times
x
equal all zeroes, What's
x
?
287. so we have the derivative of secant which is secant
x
/2 tangent
x
/2, and again completing
288. are. This
x
+2 and
x
-2 does not factor away so we have those vertical asymptotes because
289. The second
x
derivative will be 6y,
290. is (
x
, y) = (- 1; 0).
291. A function g of
x
is tilde, a function h of
x
292. the first component, which is
x
.
293. Partial v partial
x
is y. And partial v partial y is
x
.
294. And
x
is equal to negative 8.
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