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Find the extreme values of the function \(f(x, y) = x^2 + 2y^2\) on the circle \(x^2 + y^2 = 1\).
Answered
Mathematics I
Find \(\frac{∂z}{∂x} \enspace and \enspace \frac{∂z}{∂y}\) if z is defined as a function of x and y by the equation \(x^3 + y^3 + z^3 + 6xyz = 1\).
Answered
Mathematics I
If a = (4, 0, 3) and b = (-2, 1, 5) find |a|, the vector a – b and 2a + b
Answered
Mathematics I
Determine whether the series \(\sum_{n=1}^∞ \frac{n^2}{5n^2 + 4}\) converges or diverges.
Answered
Mathematics I
Find the solution of y” + 4y’ + 4 = 0.
Answered
Mathematics I
Find the volume of the resulting solid which is enclosed by the curve y = x and y = x
2
is rotated about the x-axis.
Answered
Mathematics I
Evaluate \(\int_0^∞ x^3 \sqrt{1 – x^4}\) dx
Answered
Mathematics I
Stating with x
1
= 2, find the third approximation x
3
to the root of the equation x
3
– 2x – 5 = 0
Answered
Mathematics I
Verify Mean value theorem of f(x) = x
3
– 3x + 2 for [-1, 2].
Answered
Mathematics I
Define continuity on an interval. Show that the function \(f(x) = 1 – \sqrt{1-x^2}\) on the continuous on the interval [1,-1].
Answered
Mathematics I
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