Calculus - Study Mode
[#201] The vector function [overrightarrow { ext{A}} ] is given by [overrightarrow { ext{A}} = overrightarrow
abla { ext{u,}}] xa0where u(x, y) is a scalar function, Then [left| {overrightarrow
abla imes overrightarrow { ext{A}} }
ight|]
Correct Answer
(B) 0
[#202] If [{ ext{u}} = log left( {frac{{{{ ext{x}}^2} + {{ ext{y}}^2}}}{{{ ext{x}} + { ext{y}}}}}
ight),] xa0 xa0what is the value of [{ ext{x}}frac{{partial { ext{u}}}}{{partial { ext{x}}}} + { ext{y}}frac{{partial { ext{u}}}}{{partial { ext{y}}}},?]
Correct Answer
(B) 1
[#203] Consider the plot f(x) versus x as shown below Suppose [{ ext{F}}left( { ext{x}}
ight) = int_{ - 5}^x {{ ext{f}}left( { ext{y}}
ight)} { ext{dy}}{ ext{.}}] xa0 xa0Which one of the following is a graph of F(x)?
Correct Answer
[#204] Consider the following definite integral: [{ ext{I}} = intlimits_0^1 {frac{{{{left( {{{sin }^{ - 1}}{ ext{x}}}
ight)}^2}}}{{sqrt {1 - {{ ext{x}}^2}} }}{ ext{dx}}} ] The value of the integral is
Correct Answer
(A) [frac{{{pi ^3}}}{{24}}]
[#205] The value of the directional derivative of the function [phi ](x, y, z) = xy 2 + yz 2 + zx 2 at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k is
Correct Answer
(A) 1