Derivatives
The derivative of ex sin(x)
What is ex cos(x)?
Given a bacteria culture starts with 500 bacteria and after 3 hours there are 8000, number of bacteria after t hours.
What is 800=500e3k?
Given the area of a circle is increasing at a rate of 1.5 ft2/sec with current radius of length 10 feet,
What is 1.5/(20pi)?
The value of 4.51/2 determined using the linear approximation method
What is 17/8?
Function such that f(4)=f
What is sin(x)?
The derivative of (x3+4x)1/2
What is (3x+4)*(1/2(x3+4x))?
Given a population of bacteria that grows according to the function f(t)=200e0.02t (t in minutes), bacteria are present in the population after 5 hours/300 min
What is 80,686?
The rate of change of the area of the square when the side is increasing at a rate of 3.2 feet/minute and thecurrent length of each side is 5ft.
What is 32?
The linear approximation of sinθ at θ=0
What is θ?
This statement:
"Derivative of cos/(1+sinx) is -1/(1-sinx)"
What is false?
The derivative of (3r2+1)4 where r=r(t)
If a quantity grows exponentially, the doubling time is the amount of time it takes the quantity to double given by
What is ln(2)/k?
The rate at which the distance between the top of the ladder and the ground changing when the following is given:
219 foot ladder is leaning against the wall of a very tall building. The base of the ladder is pulled away from the wall at a rate of 4.5 feet/second. At the instant that the base of the ladder is 165 feet from the base of the wall.
What is -16.61 ft/sec?
The estimated value of e0.1 using linear approximation
What is 1.1?
This Statement is:
"d2171/dx2171 2sin(x)=-2sin(x)"
What is true?
dy/dx given y3-xy=x+y
what is (x+y)/(3y2-x-1)
Given there are 200 bacteria after 2 hours and 800 bacteria after 5hours, bacteria present at time 0
What is 200/(4^(1/3))?
The rate at which the water level is falling given the following the scenario:
A large cone of given size is being drained of water at the constant rate of 15 cm3each second. The water’s surface level in the cone falls as a result.
What is -15/(16pi) cm/sec?
Estimated value of cos(18) using linear approximation
What cos(1)-sin(1)=−0.301169?
This statement:
"differentiability implies continuity"
What is false?