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The measurement of an edge of a cube is found to be 15 cm with a possible error of 0.01 cm. Find the approximate error in computing a.) the volume, b.) the area of one of the faces.
Find dy.
xy^4 + x ^ 2 y = x + 3y
Find dy.
3. sin(xy) = x ^ 2 - y
Find:Differential to approximate value of cube root of 3.3
Find the smallest positive integer N that satisfies all of the following conditions: • N is a square. • N is a cube. • N is an odd number. • N is divisible by twelve different prime numbers. How many digits does this number N have?
The formula for calculating the sum of all natural integers from 1 to n is well-known: Sn = 1 + 2 + 3 + ... + n = n 2 + n 2 Similary, we know about the formula for calculating the sum of the first n squares: Qn = 1 · 1 + 2 · 2 + 3 · 3 + ... + n · n = n 3 3 + n 2 2 + n 6 Now, we reduce one of the two multipliers of each product by one to get the following sum: Mn = 0 · 1 + 1 · 2 + 2 · 3 + 3 · 4 + ... + (n − 1) · n Find an explicit formula for calculating the sum Mn.
A space probe in the shape of the ellipsoid 62² + y² +62² = 14 enters Jupiter's atmosphere and its surface begins to heat After 1 hour, the temperature at the point (x, y, z) on the probe's surface is T(x, y, z) = 9x ^ 2 + 3yz - 18z + 600 . Find the hottest point on the probe's surface?
The velocity potential of a fluid flow given by f(x,y) = siny. Use Taylor's formula to find a quadratic approximation of f(x,y) near the point (1,1). Estimate the error in the approximation if |x_{0}| <= 0.15 and lyol ≤0.15.
If y=80x-16x2, find the difference Ay-dy if x=4 and Ax=-0.2
In a right circular cone, the radius of the base is half as long as the altitude. If an error of 2% is made in measuring the radius, find the percentage of error made in the computed volume.
