Learn more about our help with Assignments: CalculusPre-CalculusDifferential CalculusMultivariable Calculus
Search & Filtering
Calculus
This week a factory is producing 50 units of a particular commodity, and the amount being
produced is increasing at the rate of 2 units per week. If š¶(š„) dollars is the total cost of producing
š„ units and š¶(š„) = 0.08š„^3 ā š„^2 + 10š„ + 4 , find the current rate at which the production cost is increasing.
Calculus
A trough is 12 ft long and its ends are in the form of inverted isosceles triangles having an
altitude of 3 ft and a base of 3 ft. Water is flowing into the trough at the rate of 2 (ft^3/min). How fast is the water level rising when the water is 1 ft deep?
altitude of 3 ft and a base of 3 ft. Water is flowing into the trough at the rate of 2 (ft^3/min). How fast is the water level rising when the water is 1 ft deep?
Calculus
A water tank in the form of an inverted right-circular cone is being emptied at the rate
of 6m^3 / min. The altitude of the cone is 24m, and the base radius is 12m. Find how fast the water level is lowering when the water is 10m deep?
of 6m^3 / min. The altitude of the cone is 24m, and the base radius is 12m. Find how fast the water level is lowering when the water is 10m deep?
Calculus
A lonely guy throws a stone into a still pond causing a circular ripple to spread. If the radius
of the circular ripple spreads at the rate 1.5 ft/sec, how fast is the enclosed area increasing at the end of 2 seconds?
of the circular ripple spreads at the rate 1.5 ft/sec, how fast is the enclosed area increasing at the end of 2 seconds?
Calculus
A toy rocket rises vertically in such a way that t seconds after its liftoff, it is
s(t) = -16t^2 + 200t feet above the ground.
(a) How high is the rocket after 6 seconds?
(b) What is the average velocity of the rocket over the first 6 seconds of flight (between t=0 and t=6)?
(c) What is the instantaneous velocity of the rocket at t=2 sec?
s(t) = -16t^2 + 200t feet above the ground.
(a) How high is the rocket after 6 seconds?
(b) What is the average velocity of the rocket over the first 6 seconds of flight (between t=0 and t=6)?
(c) What is the instantaneous velocity of the rocket at t=2 sec?
Calculus
Suppose a person standing at the top of a building 112 ft high throws a ball vertically upward
with an initial velocity of 96 ft/sec.
(a) Find the velocity of the ball at time
with an initial velocity of 96 ft/sec.
(a) Find the velocity of the ball at time
Calculus
A car is travelling at 100 ft/sec when the driver suddenly applies the brakes. The position
function of the skidding car is
function of the skidding car is
Calculus
An object moves along a straight line so that after š” minutes, its distance from its starting point
is š (š”) = 10t + (5/t+1) - 5 meters.
(a) At what speed is the object moving at the end of 4 minutes?
(b) How far does the object actually travel during the 5th minute?
(c) How fast is its velocity changing at š” = 6 ššš?
Calculus
Derive a formula for
n
ā
i= iĀ² a telescoping sum with terms f(I) = iĀ³
n
ā (3i-1)Ā²
i=1
n
ā (2i + 1)Ā²
i=1
n
ā
i= iĀ² a telescoping sum with terms f(I) = iĀ³
n
ā (3i-1)Ā²
i=1
n
ā (2i + 1)Ā²
i=1
Calculus
A pendulum swing through an arc of length 54cm. On each successive swing, the length
of the arc is 0.92 of the previous length.
(a) What is the length of the arc after 7 swings.
(b) At which swing is the length of the arc of the pendulum less than 17cm for the
first time.
(c) Find the total distance covered by the pendulum after 22 swings.
(d) Find the total distance covered by the pendulum before it comes to a stop.
of the arc is 0.92 of the previous length.
(a) What is the length of the arc after 7 swings.
(b) At which swing is the length of the arc of the pendulum less than 17cm for the
first time.
(c) Find the total distance covered by the pendulum after 22 swings.
(d) Find the total distance covered by the pendulum before it comes to a stop.
