Calculus - Study Mode
[#161] The divergence of the vector field [overrightarrow {
m{U}} = {{
m{e}}^{
m{x}}}left( {cos ,{
m{yhat i}} + sin {
m{yhat j}}}
ight)] xa0 xa0 is
Correct Answer
(C) 2e x cos y
[#162] Given a function f(x, y) = 4x 2 + 6y 2 - 8x - 4y + 8. The optimal value of f(x, y)
Correct Answer
(A) is a minimum equal to [frac{{10}}{3}]
[#163] To evaluate the double integral [int_0^8 {left( {int_{frac{{ ext{y}}}{2}}^{frac{{ ext{y}}}{2} + 1} {left( {frac{{2{ ext{x}} - { ext{y}}}}{2}}
ight){ ext{dx}}} }
ight){ ext{dy,}}} ] xa0 xa0 xa0we make the substitution [{ ext{u}} = frac{{2{ ext{x}} - { ext{y}}}}{2}] xa0 and [{ ext{v}} = frac{{ ext{y}}}{2}.] xa0The integral will reduce to
Correct Answer
(B) [int_0^4 {left( {int_0^1 {2{ ext{u du}}} }
ight){ ext{dv}}} ]
[#164] [iint {left( {
abla imes { ext{P}}}
ight) cdot { ext{ds,}}}] xa0 xa0where P is a vector, is equal to
Correct Answer
(A) [oint {{ ext{P}} cdot { ext{d}}l} ]
[#165] [mathop {{ ext{Lim}}}limits_{{ ext{x}} o 0} frac{{sin { ext{x}}}}{{ ext{x}}}] xa0 is
Correct Answer
(C) 1