Find the equation of the function whose tangent has a slope 6/x^2 for each value of x and whose graph passes through the point (2,5).
What is f(x)= -6/x + 8
200
∫2/2x+1 dx
What is ln|2x+1|+C
200
∫2/6x-5 dx
What is 1/3ln|6x-5| +C
200
∫5e^5x dx
What is e^5x+C
200
∫x^3 e^2x dx
What is 1/2x^3 e^2x - 3/4x^2 e^2x + 3/4xe^2x - 3/8e^2x +C
200
Find the equation of the function f whose tangent has a slope x/(x^2-5)^2 for each value of x and whose graph passes through the point (2,1).
What is f(x)= -1/2(x^2-5) + 1/2
300
∫3x^2/x^3 dx
What is ln|x^3|+C
300
∫3/(6x-5)^3 dx
What is -1/4(6x-5)^2 +C
300
∫(e^x-x) dx
What is e^x-x^2/2+C
300
∫5x-4/x^2 -4x dx
What is ln|x| + 4ln|x-4| +C
300
Find the function whose tangent has a slope x^3 -2/x^2 +2 for each value of x and whose graph passes through the point (1,3).
What is f(x)= 1/4x^4 + 2/x + 2x - 5/4
400
∫1/4x+1 dx
What is ln|4x+1|/4+C
400
∫(x^2 -3x)^5 (4x-6) dx
What is (x^2 -3x)^6/3 +C
400
∫e^2x+3 dx
What is 1/2e^2x+3+C
400
∫3x^2 -7x -2/x^3 -x dx
What is 2ln|x| -3ln|x-1|+4ln|x+1| +C
400
A car can accelerate from a standing start to a speed of v(t)=-.09t^2 + 6t feet per second after t seconds (for t<40). Find a formula for the distance that it will travel from its starting point in the first t seconds. Use the formula to find the distance that the car will travel in the first 10 seconds.
What is 270 feet.
500
∫3x/x^2+4 dx
What is 3ln|x^2+4|/2+C
500
∫24/e^2/3x dx
What is -36/e^2/3x +C
500
∫4xe^x^2 dx
What is 2e^x^2+C
500
∫x^2 +12x +12/x^3 -4x dx
What is -3ln|x| +8ln|x-2| -ln|x+2| +C
500
The marginal revenue for the sale of a product can be modeled by dR/dx= 45-.04x+150/x+2 where x is the quantity demanded. Find the revenue when 2000 units are sold. Assume the revenue is zero when the production and sales level is zero.