Calculus - Study Mode
[#196] How many distinct values of x satisfy the equation sin(x) = [frac{{ ext{x}}}{2}], where x is in radians?
Correct Answer
(C) 3
[#197] The [mathop {lim }limits_{{ ext{x}} o 0} frac{{sin left[ {frac{2}{3}{ ext{x}}}
ight]}}{{ ext{x}}}] xa0 is
Correct Answer
(A) [frac{2}{3}]
[#198] The value expression [mathop {lim }limits_{{ ext{x}} o 0} frac{{sin { ext{x}}}}{{{{ ext{e}}^{ ext{x}}}{ ext{x}}}}] xa0is
Correct Answer
(C) 1
[#199] Assuming [{ ext{i}} = sqrt { - 1} ] xa0 and t is a real number, [intlimits_0^{frac{pi }{3}} {{{ ext{e}}^{{ ext{it}}}}} { ext{dt}}] xa0 is
Correct Answer
(A) [frac{{sqrt 3 }}{2} + { ext{i}}frac{1}{2}]
[#200] If [{ ext{f}}left( { ext{x}}
ight) = { ext{R}}sin left( {frac{{pi { ext{x}}}}{2}}
ight) + { ext{S}},{ ext{f}}'left( {frac{1}{2}}
ight) = sqrt 2 ] xa0 xa0 xa0 and [intlimits_0^1 {{ ext{f}}left( { ext{x}}
ight){ ext{dx}} = frac{{2{ ext{R}}}}{pi }} ,] xa0 xa0 then the constants R and S are, respectively
Correct Answer
(C) [frac{4}{pi }] and 0