Calculus - Study Mode
[#146] Let [phi ] be an arbitrary smooth real valued scalar function and V be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?
Correct Answer
(C) [{ ext{Div Curl }}overrightarrow { ext{V}} = 0]
[#147] The magnitude of the directional derivative of the function f(x, y) = x 2 + 3y 2 in a direction normal to the circle x 2 + y 2 = 2, at the point (1, 1), is
Correct Answer
(A) 4√2
[#148] If $${ ext{S}} = intlimits_1^infty {{{ ext{x}}^{ - 3}}{ ext{dx,}}} $$ xa0 then S has the value
Correct Answer
(C) $$frac{1}{2}$$
[#149] By a change of variable x(u, v) = uv, y(u, v) = v/u is double integral, the integrand f(x, y) changes to f(uv, v/u) [phi ] (u, v). Then, [phi ] (u, v) is
Correct Answer
(A) 2 u/v
[#150] Which one of the following describes the relationship among the three vectors, [{
m{hat i}} + {
m{hat j}} + {
m{hat k}},,2{
m{hat i}} + 3{
m{hat j}} + {
m{hat k}}] xa0 xa0 and [{
m{5hat i}} + 6{
m{hat j}} + 4{
m{hat k}},{
m{?}}]
Correct Answer
(B) The vectors are linearly dependent