Limits
Find
lim_(x->3)3x^2-2x
21
In a race of 8 runner, 3 receive a medal: gold, silver and bronze. How many possibilities are there?
336
Expand (x-y)3
x3-3x2y+3xy2-y3
Write the rule of the sequence for 3,4,5,6,7,...
an=n+3
Write the equation of a circle with center (3,-6) and radius 7.
(x-3)^2+(y+6)^2=49
lim_(x->pi) cosx
-1
In a race of 12 runners, 6 advance to the final. How many possibilities are there?
924
Expand (2x+y)3
8x3+12x2y+6xy2+y3
Write the rule of the sequence: 1/5, 1/6, 1/7, 1/8, ...
an=1/(n+4)
Put in standard form
4x^2-16x+9y^2+18y-11=0
(x-2)^2/9+(y+1)^2/4=1
lim_(x->5)(x^2-2x-15)/(x^2+x-30)
8/11
In a standard deck of cards, what is the probability of choosing a heart or a 10?
4/13=0.3077
Expand (3x+1)4
81x4+108x3+54x2+12x+1
Write the explicit and recursive rule for the arithmetic sequence where a5=28 and a9=52
an=4+6(n-1)
a1=4, an=an-1+6
Find the asymptotes of
(x-5)^2/4-(y-7)^2/1=1
y=9/2+1/2x, y=19/2-1/2x
f(x)=8x-9, lim_(h->0)(f(x+h)-f(x))/h
8
In a standard deck of cards, what is the probability of choosing a face card or an Ace?
4/13=0.3077
Expand (4x+2)4
256x4+512x3+384x2+128x+16
Write the explicit and recursive rule for the arithmetic sequence where a3=-1 and a11=-17
an=3-2(n-1)
a1=3, an=an-1-2
Put in standard form:
x^2+y^2+12x-2y+25=0
(x+6)^2+(y-1)^2=12
lim_(x->0)(sqrt(x+1)-1)/x
1/2
In a standard deck of cards, what is the probability of choosing a non-face card or club?
43/52=0.8270
Expand (2x-3y)5
32x5-240x4y+720x3y2-1080x2y3+810xy4-243y5
Write the explicit and recursive rule for the geometric sequence where a2=12 and a5=768
an=3*4n-1
a1=3 an=4*an-1
Find the center, vertices, foci, and eccentricity of
(x-2)^2/9+(y+1)^2/36=1
Center: (2,-1)
Vertices: (2,5) and (2, -7)
Eccentricity:
sqrt27/6
Foci:
(2,-1+sqrt27), (2, -1-sqrt27)