a = [0, 2, 3], b = [-1, 2, 1] a × b =
c = [3, 4], r = [-1, 0] (c, r) =
(2, 1, -3) [2, 0, -1]
y+2
x-1 z
= =
-2 3 4
m, f t
f Df =R\{2}, lim f(x)=-"
x2
n3-2n+1
lim =
2-5n2
n"
(x-3)
lim =
3-x
x3
lim (1 + 2 sin x) (x) =
x0+
f a, b fab = fba
T R3 T =
1 x2 +y2 3, y x, x 0
f(x, y)dxdy D
D
y = ex, y = 2x, x = 4
ln x
f(x) =
2x
" "
4
(y +4x2)dC C C : x(t) = t, y(t) = 3 - t
C
S (1, 0, 0), (1, 1, 0), (1, 0, 1)
OX (x + y)dydz + 3yxdzdx - xydxdy
S
 a = [1, 0, -3], b = [2, , 21] b × a =
c = [-4, 3], r = [3, 0] (c, r) =
(1, 3, -4) [0, 3, -2]
y-2
x+3 z
= =
1 -4 2
r, s q
f Df =R\{-1}, lim f(x)="
x-1
3n2-2n+1
lim =
n-4n2
n"
(x+1)
lim =
2x+2
x-1
lim (1 - 2 sin x) (x) =
x0-
f m, n fmn = fnm
P R2 P =
1 x2 +y2 5, y x, x 0
f(x, y)dxdy D
D
y = ln x, y = log1 x, x = 3
2
x
f(x) =
ex
" "
4
C C : x(t) = t, y(t) = 5 - t
(y + 4x2)dC C
C
(x+y)dydz +3yxdzdx-xydxdy S
S
(2, 0, 0), (2, 1, 0), (2, 0, 1) OX
liczba liter w imieniu
©
liczba liter w nazwisku
q = [2, 1, -1], c = [0, , ©], t = [-1, 2, 1] (2 t - c) × q =
Ä„
v = [ , ©], m = [-1, 1] (v, m)
2
(2, ©, -3)
( , -3, 0) [-3, 0, ©]
3n© + 3n - 4
lim = ...
n" - 7n©
1
©x - ·©
lim = ...
+
log(x - )
x
lim(1 - ©x) (x) = ...
x0
T R3 " · T = ...
8
1
e8 arccos 0 arccos
©
( +©) ( ·©) ln 17 log© 17
g(x, y)dxdy M
M
y = x3, y = 2 - x, x = -
+©x
f(x) =
x2+2x+1
x2 + y2 +©, y x, y -x
ydx + sinxdy AB A = (- , 1)
AB
B = (©, 1)
exy-zdS S x2 + y2 + z2 = © z 0
S
f