`frac{4}{3} -: ?=frac {-5}{2}`

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

3frac{1}{13}+1frac{4}{13}+2frac{3}{13}

frac{dP}{dx} = frac{d}{dx} (x^3) (frac{7-2x}{3})^(4)

Prove that Cos frac{pi}{5} + Cos frac{2pi}{5} + Cos frac{6pi}{5} + Cos frac{7pi}{5} = 0

\lim _{x\to 0}(\frac{1}{e^x-1}-\frac{1}{x}\)

If z(x+y)= x^2 +y^2 show that (frac{delz}{delx}-frac{del z}{del y})^2 = 4 (1- frac{delz}{delx}+frac{delz}{dely})

frac{1}{sqrt7-4} frac{1}{sqrt11-7}

If force on a particle vecF = (Sin at)hati + (cos at)hatj and displacement vecS = sin(frac{at}{3}hati) + cos(frac{at}{3})hatj are functions of time (t) then value of t at which they are perpendicular for first time is (a is positive constant and t>0)

cos frac{3pi}{4}-iota sin frac{3pi}{4}

x frac{dy}{dx} = y - xcos^2 frac{y}{x}