Intergrals
(no calc)
(no calc)
y1 = e7x
(1/7)e7x + c
y= ln(10x)
y1= (1/x)
lim (x2-3x+2) / (x-1)
x → 1
lim (-1)
x → 1
Critical Points:
y= x4-2x2
(-1,0) (1,0) (0,0)
Suppose that when a hockey player strikes a puck with a certain force, the puck mores along the ice with a velocity V(t) = 64 - (t)1/2 ft/sec at time (t) for the first 8 seconds. Determine distance between the puck and the player after 5 seconds.
d (5) = 312.54
y1= (cos3x)4sin3x
y= (1/15)(cos3x)5 + c
y= sin(ln(6x))
y1= cos(ln(6x))
x
lim (x2+x-2) / (x2-4)
x → -2
lim (3/4)
x → -2
L’hopitals Rule:
lim (lnx) / (x2-1)
x → 1
lim (1/2)
x → 1
Homer and Marge foolishly gave their children 6 rabbits for Easter. The rabbits double in number every 3 months, at what rate is the rabbit population increasing after 2 years?
y1= 355
y= 2x3ln4x
y1= 2x2(3ln4x+1)
lim (sin2x) / (x)
x → 0
lim (2)
x → 0
Implicit Differentiation:
y5-7xy-18x3=3
y1= (-7y-54x2) / (-5y4+7x)
Ms Denny blows up a spherical balloon and then releases it so its air is expelled like a rocket. If the radius of the balloon decrease at a rate of 2cm/s how fast is its volume decreasing when the radius equals 12?
dv/dt = -1152πcm3/sec
y= (4x)(tan3x)
y1= 4x(ln4tan3x + 3sec23x)
lim (6x2-3x+7) / (11x2+3)
x → ♾
lim (6/11)
x → ♾
Tangent Line:
x2+ y3- 2y = 3 (2,1)
y-1=-4(x-2)
A population of insects is growing at a rate described by P1(t)= 50sin(π/4)t insects per month where t is the number of months since March 1st. If the insect population is 600 on April 1st determine the population on August 1st.
~ 690
y= x4x
y1= 4(lnx + 1) x4x
lim (2x-1) - 4 / (x-3)
x → 3
lim 2.77
x → 3
Concavity:
y= 4x3+21x2+36x-20
x= (-7/4)
A juice can is to hold 1.2 L (1200 cm3). The material used to make the bottom and top of the can is triple the price per cm2 of the material used for the can wall. Use calculus methods to find the dimensions (to the nearest hundredth of a cm) that will minimize the cost of material required to manufacture the can.
Radius of 3.99cm and a Height of 23.99cm, will minimize the cost