Jill and Ellingtons Jepordy

Intergrals(no calc)

100

y¹ = e^7x

(1/7)e^7x + c

200

y¹= (cos3x)⁴sin3x

y= (1/15)(cos3x)⁵ + c

Derivatives

100

y= ln(10x)

y¹= (1/x)

200

y= sin(ln(6x))

y¹= cos(ln(6x))

             x

300

y= 2x³ln4x

y¹= 2x²(3ln4x+1) 

400

y= (4^x)(tan3x)

y¹= 4^x(ln4tan3x + 3sec²3x)

500

y= x^4x

y¹= 4(lnx + 1) x^4x

Limits

100

lim (x²-3x+2) / (x-1)

  x → 1

lim (-1)

x → 1

200

lim (x²+x-2) / (x²-4)

x → -2

lim (3/4)

x → -2

300

lim (sin2x) / (x)

x → 0

lim (2)

x → 0

400

lim (6x²-3x+7) / (11x²+3)

x → ♾

lim (6/11)

x → ♾

500

lim (2^x-1) - 4 / (x-3)

x → 3

lim 2.77

x → 3

Pot Purri

100

Critical Points:

y= x⁴-2x²

(-1,0) (1,0) (0,0)

200

L’hopitals Rule:

 lim (lnx) / (x²-1)

x → 1

lim (1/2)

x → 1

300

Implicit Differentiation: 

y⁵-7xy-18x³=3

y¹= (-7y-54x²) / (-5y⁴+7x)

400

Tangent Line:

x²+ y³- 2y = 3 (2,1)

y-1=-4(x-2)

500

Concavity:

y= 4x³+21x²+36x-20

x= (-7/4) 

Applications

100

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

200

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

300

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

400

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

500

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