Calculus Answers

Find the most economical dimensions for a closed cylindrical can containing a quart.

If an apple is launched out of a fruit cannon vertically upward from ground level with an initial velocity of 80 feet per second, then its height h after t seconds is given by the equations h(t)= -16t²+80t (if air resistance is neglected). How long will it take for the apple to return to the ground?

Find all values of x where the function f(x)=-4x^2/e^-4x has a relative maximum. If there are no such values of x, submit an empty answer.

Let X be a non-empty set of real numbers. If it has a greatest lower bound, then it must be unique

the current is given by i=e^(-t * R/L) where R is the resistance in ohms, L is the inductance in henrys and t is the time in seconds. Calculate the rate of change of current, if the resistance decreases at 2Ohms, the inductance increases at 0.2 H/s at the instance when t=0.01s, L=0.5H and R=30Ohms

Let α and β be two real numbers so that α ≤ β and β ≤ α. Then α = β.

Prove.

Let Q=(1/R) * sqrt(L/C)

Suppose that L decreases by 2.8%. R decreases by 3.5% and C increases by 5%. Use the small increments method to calculate the percentage in Q. Is the change an increase, a decrease or does Q remain unchanged? Give reasons for your answers.

a curve is defined parametrically by the equations x=2sintheta y=cos^2(theta) find the equation of the tangent to this curve at (2;0)

Every rational number can be expressed as a quotient p/q so that p and q has no common factors.

Let a,x and y are real numbers so that x < y and a > 0. Then ax < ay.

Priove.