Questions from General Calculus

Q: The radius of a circular disk is given as 24 cm with

The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (b) What is the r...

Q: The circumference of a sphere was measured to be 84 cm with

The circumference of a sphere was measured to be 84 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. What is the relative error?...

Q: A plane flies horizontally at an altitude of 5 km and passes

A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of  π/6 rad/min....

Q: Use differentials to estimate the amount of paint needed to apply a

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 50 m.

Q: (a) Use differentials to find a formula for the approximate

(a) Use differentials to find a formula for the approximate volume of a thin cylindrical shell with height h, inner radius r, and thickness Dr. (b) What is the error involved in using the formula from...

Q: One side of a right triangle is known to be 20 cm

One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°, with a possible error of 61°. (a) Use differentials to estimate the error in computing the length of t...

Q: A manufacturer produces bolts of a fabric with a fixed width.

A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write...

Q: If a current I passes through a resistor with resistance R,

If a current I passes through a resistor with resistance R, Ohm’s Law states that the voltage drop is V = RI. If V is constant and R is measured with a certain error, use differentials to show that th...

Q: When blood flows along a blood vessel, the flux F (

When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel: F − kR4 (Th...

Q: Suppose that the only information we have about a function f is

Suppose that the only information we have about a function f is that f (1) = 5 and the graph of its derivative is as shown. (a) Use a linear approximation to estimate f (0.9) and f (1.1). (b) Are you...