Related Rates
A ladder 10 ft long leans against a wall. The bottom slides away at 1 ft/sec. How fast is the top sliding down when the bottom is 6 ft from the wall?
Find two numbers whose sum is 10 and whose product is as large as possible.
What is a differential equation?
An equation involving derivatives that describes a relationship between a function and its rates of change.
Find the area between y=x and y=x^2 from x=0 to x=1
State the Fundamental Theorem of Calculus, Part 1.
A balloon is rising at 3 m/s. A person is 50 m away horizontally. How fast is the distance between them changing when the balloon is 40 m high?
Find the dimensions of a rectangle with perimeter 36 units that has the maximum area.
Given [dy/dx]=2x, find the general solution.
Find the are enclosed between y=sqrt(x) and y=x from 0 to 1
Water pours into a conical tank at 5 m³/min. The tank’s height is 10 m, radius is 5 m. How fast is the water level rising when the water is 4 m deep?
What is the minimum distance from the point (0, 0) to the parabola y=x^2 - 4
Solve [dy/dx] = 3y using separation of variables.
Find the volume generated by rotating y=x^2 abt the x-axis from 0 to 1
A camera tracks a car moving along a straight road at 30 m/s. The camera is 12 m from the road. How fast must it rotate when the car is 16 m away?
Find the dimensions of a cylindrical can that holds 1000 cm³ and uses the least amount of material (minimize surface area).
Match the slope field to the differential equation:
A. [dy/dx]=y,
B. [dy/dx]=x,
C. [dy/dx]=-y
Use the washer method to find the volume of the region between y=sqrt(x) and y=0 rotated abt the x-axis from 0 to 4
Two ships leave port at noon, one sailing east at 20 km/h and the other north at 15 km/h. How fast is the distance between them changing at 3 PM?
A window has a rectangular bottom and a semicircular top. If the perimeter is 20 m, what dimensions maximize the area?
Solve the initial value problem:
[dy/dx]=(xy)/4, with y(0)=2
Use the shell method to find the volume of the region bounded by a y=x, y=0, and x=2, rotated about the y-axis