Questions from General Calculus

Q: Find the point on the hyperbola xy = 8 that is closest

Find the point on the hyperbola xy = 8 that is closest to the point (3, 0).

Q: Find the smallest possible area of an isosceles triangle that is circumscribed

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r.

Q: (a). Use an improper integral and information from Exercise 27

(a). Use an improper integral and information from Exercise 27 to find the work needed to propel a 1000-kg satellite out of the earth’s gravitational field. Exercise 27: (a). Newto...

Q: Find the volume of the largest circular cone that can be inscribed

Find the volume of the largest circular cone that can be inscribed in a sphere of radius r.

Q: In lies on ∆ABC, D, lies on AB,

In lies on ∆ABC, D, lies on AB, |CD| = 5cm, |AD| = 4 cm, |BD = 4cm, and CD ⊥ AB. Where should a point p be chosen on CD so that the sum |PA| + |PB| + |PC| is a minimum? What if |CD| = 2 cm?

Q: A solid is generated by rotating about the -axis the region

A solid is generated by rotating about the -axis the region under the curve y = f (x), where f is a positive function and x > 0. The volume generated by the part of the curve from x = 0 to x = b is b2...

Q: Find the approximations Ln, Rn, Tn and Mn for n

Find the approximations Ln, Rn, Tn and Mn for n = 5, 10 and 20. Then compute the corresponding errors EL, ER and ET. and EM (Round your answers to six decimal places. You may wish to use the sum comma...

Q: If f (x) = fg(x)01/√

If f (x) = fg(x)01/√1 + t3, dt, where g (x) = fcosx0[1 + sin (t2)], dt, find f'(π/2).

Q: A string is wound around a circle and then unwound while being

A string is wound around a circle and then unwound while being held taut. The curve traced by the point P at the end of the string is called the involute of the circle. If the circle has radius r and...

Q: For what value of a is the following equation true?

For what value of a is the following equation true?