Calculus - Study Mode
[#171] Which of the following integrals is unbounded?
Correct Answer
(D) [intlimits_0^1 {frac{1}{{1 - { ext{x}}}}{ ext{dx}}} ]
[#172] Changing the order of the integration in the double integral [{ ext{I}} = intlimits_0^8 {intlimits_{frac{{ ext{x}}}{4}}^2 {{ ext{f}}left( {{ ext{x,}},{ ext{y}}}
ight){ ext{dydx}}} } ] xa0 xa0 leads to [{ ext{I}} = intlimits_{ ext{r}}^{ ext{s}} {intlimits_{ ext{p}}^{ ext{q}} {{ ext{f}}left( {{ ext{x,}},{ ext{y}}}
ight){ ext{dx dy}}} .} ] xa0 xa0 What is q?
Correct Answer
(A) 4y
[#173] The divergence of the vector field [overrightarrow {
m{A}} = {
m{x}}{{{
m{hat a}}}_{
m{x}}} + {
m{y}}{{{
m{hat a}}}_{
m{y}}} + {
m{z}}{{{
m{hat a}}}_{
m{z}}}] xa0 xa0is
Correct Answer
(D) 3
[#174] Compute [mathop {lim }limits_{{ ext{x}} o 3} frac{{{{ ext{x}}^4} - 81}}{{2{{ ext{x}}^2} - 5{ ext{x}} - 3}}]
Correct Answer
(A) [frac{{108}}{7}]
[#175] The angle (in degree) between two planes vectors [overrightarrow {
m{a}} = frac{{sqrt 3 }}{2}{
m{hat i}} + frac{1}{2}{
m{hat j}}] xa0 xa0and [overrightarrow {
m{b}} = frac{{ - sqrt 3 }}{2}{
m{hat i}} + frac{1}{2}{
m{hat j}}] xa0 xa0is
Correct Answer
(D) 120