Engineering Mat...

Consider a function f = y^x, then the value of \(\left( {\frac{{{\partial ^2}f}}{{\partial x\partial y}}} \right)\) at point (2, 1) is -

If R is the region 0 ≤ x ≤ y ≤ L, then

\(\mathop \int\!\!\!\int \limits_R \left( {{x^2} + {y^2}} \right)dx\;dy\) is

Which one of the following integrals is NOT an improper integral?

The value of \(\mathop \smallint \limits_0^{\frac{\pi }{2}} \mathop \smallint \limits_0^{\frac{\pi }{2}} \mathop \smallint \limits_0^5 \sin \theta d\theta \;d\phi \;dr\) expressed in spherical co-ordinate will be ______ π.

If Z = e^{ax + by} F(ax - by); the value of \(b\frac{{\partial Z}}{{\partial x}} + a\frac{{\partial Z}}{{\partial y}}\) is

The time period of simple pendulum is \(T = 2\pi \sqrt {\frac{l}{g}}\). Find maximum error % in T due to possible error upto 1% in l and 2.5% in g.