Solve Rate of Change Problems in Calculus
Rate of change calculus problems and their detailed solutions are presented.
Problem 1A rectangular water tank (see figure below) is being filled at the constant rate of 20 liters / second. The base of the tank has dimensions w = 1 meter and L = 2 meters. What is the rate of change of the height of water in the tank?(express the answer in cm / sec).Solution to Problem 1:
Problem 2An airplane is flying in a straight direction and at a constant height of 5000 meters (see figure below). The angle of elevation of the airplane from a fixed point of observation is a. The speed of the airplane is 500 km / hr. What is the rate of change of angle a when it is 25 degrees? (Express the answer in degrees / second and round to one decimal place).Solution to Problem 2:
Problem 3If two resistors with resistances R1 and R2 are connected in parallel as shown in the figure below, their electrical behavior is equivalent to a resistor of resistance R such thatIf R1 changes with time at a rate r = dR1/dt and R2 is constant, express the rate of change dR / dt of the resistance of R in terms of dR1/dt, R1 and R2. Solution to Problem 3:
Exercises1 - Find a formula for the rate of change dV/dt of the volume of a balloon being inflated such that it radius R increases at a rate equal to dR/dt.2 - Find a formula for the rate of change dA/dt of the area A of a square whose side x centimeters changes at a rate equal to 2 cm/sec. 3 - Two cars start moving from the same point in two directions that makes 90 degrees at the constant speeds of s1 and s2. Find a formula for the rate of change of the distance D between the two cars. Solutions to the Above Exercises1 - dV/dt = 4*Pi*R^{ 2}dR/dt2 - dA/dt = 4x cm^{ 2}/sec 3 - dD/dt = sqrt( s1^{ 2} + s2^{ 2} ) More references on calculus problems |