Derivatives
The derivative of 2x-5
What is 2?
The integral of x+1dx
What is x2+x+C ?
Lim x->1 (x2-2x+1)
What is 0?
The solution to the differential equation dy/dx=4x+5y
What is y=-4/5x-25/4 ?
The amount of money in my bank account one year after I make an initial deposit of $1,000 with 7% interest compounded monthly.
What is $1072.29 ?
The derivative of 4x3-13x2+8x
What is 12x2-26x+8?
The integral of 3/(x+9)dx
What is 3ln(x+9)+C?
lim x->-3 (x2-9)/(x2+3x-18)
What is -2?
The rate that money $ flows into a bank account is directly proportional to the value of total sales in $ times the number of hours, t, worked by Worker X.
What is d$/dt=$t ?
The amount of garbage in a landfill after 5 years of continuously growing 25% if it originally had 7,438 pieces of trash.
What are 25,961 pieces of trash?
The derivative of 4x2(4-x)
What is 32x-12x2?
The integral of ln(x)dx
What is xln(x)-x+C?
The lim x->-infinity x1/3-7x2+14x
What is -infinity?
True or false: y=-ex^2-6x is a solution to the differential equation dy/dx=y(2x-6)
What is true?
The initial amount of an element X (half-life=50 years) if only 4.68g are left after 100 years of radioactive decay.
What is 18.72g of element X?
The derivative of 4arctan(x2+2)
What is 8x/((x2+2)2+1)?
The integral of (x-1)/(sqrt(x2-2x+4))dx
What is sqrt(x2-2x+4)+C?
The limit x->infinity (6+x-3x2)/(5+x2+9x4)1/2
What is -1?
The solution y=f(x) to dy/dx=x2y+3 when f(1)=0
What is y=-7/3ex^3/3+3x ?
The time in years it will take for 99% of a 150.39g sample of Radon (half-life 3.8 days) to decay.
What is .069 years?
The derivative of (9x3+18x)/(3x2+3)
What is 3(x4+x2+2)/(x2+1)2 ?
The integral of excos(2x)dx
What is ex(2sin(2x)+cos(2x)/5+C?
The limit x->-infinity (6+x-3x2)/(5+x2+7x4)1/2
What is -3/71/2?
The position equation for a falling object pushed off a 40m cliff whose acceleration due to gravity is -9.8 m/s2 and the velocity of the object is -2 m/s when t=0.
What is P(t)=1/2(-9/8)t2-2t+40 ?
What is 7.09 degrees Celsius?