Questions from General Calculus

Q: For what values of r does the function y=erx satisfy

For what values of r does the function y=erx satisfy the differential equation y’’ - 4y’ + y=0?

Q: Find the 1000th derivative of f (x)=xe-x

Find the 1000th derivative of f (x)=xe-x.

Q: Let f (x) = cx + ln (cos x

Let f (x) = cx + ln (cos x). For what value of c is f ‘(π/4) = 6?

Q: The displacement of a particle on a vibrating string is given by

The displacement of a particle on a vibrating string is given by the equation s(t) = 10 + 1/4 sin(10πt) where s is measured in centimeters and t in seconds. Find the velocity of the particle after t s...

Q: If the equation of motion of a particle is given by s

If the equation of motion of a particle is given by s = A cos (ωt + δ), the particle is said to undergo simple harmonic motion. (a) Find the velocity of the particle at time t. (b) When is the velocit...

Q: The motion of a spring that is subject to a frictional force

The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine func...

Q: Find the nth derivative of each function by calculating the first few

Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

Q: The average blood alcohol concentration (BAC) of eight male subjects

The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption of 15 mL of ethanol (corresponding to one alcoholic drink). The resulting data were modeled by the c...

Q: In Section 1.4 we modeled the world population from 1900

In Section 1.4 we modeled the world population from 1900 to 2010 with the exponential function P(t) = (1436.53) . (1.01395)t where t = 0 corresponds to the year 1900 and Pstd is measured in millions....

Q: How many tangent lines to the curve y = x/(x

How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do these tangent lines touch the curve?