Calculus Answers

A communication signal is given by the function =sin⁡t/t . Derive an equation for dy/dt using the Quotient Rule.

find out the volume of hemi sphere of radius R using spherical polar co ordinate system.

Which of the following is true regarding the series ∑nr=1e1−r
Hint: write out the first few terms of the series to understand it better

A. This series is not a geometric series.
B. ∑r=1ne1−r=en−1e−1
C. limn→∞∑r=1ne1−r=ee−1
D. The series is a telescoping series

What is the first approximation of the function f(x)=(1−x)100 near x=0?

A producer of perishable product offers a wage incentive to drivers of its truck. A standard delivery
takes an average of 20 hours. Drivers are paid at the rate of $15 per hour up to a maximum of 20 hours.
If the trip requires more than 20 hours, the drivers receive compensation for only 20 hours. There is
an incentive for drivers to make the trip in less (but not too much less!) than 20 hours. For each hour
under 20, the hourly wage increase by $2.5.
(a) Determine the function w =f(x) where w equals the hourly wage in dollars and x equals the
number of hours required to complete the trip.
(b) What trip time x will maximize the drivers salary for a trip?
(c) What is the hourly wage associated with the trip time?
(d) What is the maximum salary?
(e) How does this salary compare with that received for a 20-hour trip?

Determine the concavity of the parabola representing the quadratic function, its y intercept, its x
intercept if any exist, and the coordinates of the vertex. Sketch the parabola. Y = 25x
2 +8x-12.

Find the range of the function f defined by f(x y)=10-x^2-y^2 for all (x y) for which x^2+y^2<=9. Sketch two of its level curves.

show that surface a integral =48pi where a=4xi-2y^2j+z^2k and s is curved surface of cylinder x^2+y^2=4 bounded by plane z=0 to 3

A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. if the pentagon has fixed perimeter P, find the lengths of the sides of the pentagon that maximize the area of the pentagon

What is the first approximation of the function f(x)=(1−x)^100 near x=0?