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The altitude of a certain right circular cone is the same as the radius of the base, and is measured as 5 inches with a possible error of 0.02 inch. Find approximately the percentage error in the calculated value of the volume.
Find the differential of y=(x+a)²
Find the differential of y=3√6x
Find the differential of y=x³-2x²+5
A conical cistern is 10 ft across the top and 12 ft deep. If water is poured into the cistern at the rate of 1 cubic foot per second, how fast is the surface rising when the water is 8 ft deep?
A light hang 15 ft directly above a straight walk on which a man 6 ft tall is walking. How fast is the end of the man's shadow traveling when he is walking away from the light at a rate of 3 miles per hour?
The base of an isosceles triangle is 8 feet kong. If the altitude is 6 feet long and increasing 3 inches per minute, at what rate are the base angles changing?
One ship is sailing south at a rate of 5 knots, and other is sailing east at a rate of 10 knots. At 2 pm, the second ship was at the place occupied by the first one hour before. At what time was the distance between the ships not changing?
Exercise 1. Every rational number can be expressed as a quotient p/q so that p and q has no common factors.
Evaluate the integrals
i) "\\int_{s}^{}\\overrightarrow{F} \\overrightarrow{ds}"
ii) "\\int_{s}^{}\\overrightarrow{F} \\times \\overrightarrow{ds}"
"\\overrightarrow{F} = ( x^2 +y , y + z , z + x)" and s is the square 0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑧 ≤ 2 and 𝑦 = 0 positively oriented along the positive Y-axis.
