Find the height of a right cylinder with greatest lateral surface area that may be inscribed in a given sphere of radius R.
Let the right circular cylinder be inscribed in a sphere of radius \( R \). Denote the cylinder’s height as \( h \) and its base radius as \( r \). The cylinder fits inside the ________ ______ ___ ______ _________ _________ __________ ________.
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Prove that
Find the angle between the vectors and
.
Reduce the equation
xy" + y' + xy = 0, x > 0
into Bessel's equation and hence write its general solution in terms of Bessel's functions.
Can Rolle's theorem be applied to each of the following functions? Find 'c' in case it can be applied.
i. f(x) = sin2 x on the interval [0, π].
ii. f (x) = x² + 4 on [-2, 2].
iii. f(x) = sinx + cos x on
iv. f(x) = x³- 2x on [0, 1].
Find and
for the function x² sin(y³)+xe3z-cos(z²)=3y-6z+8