lim_(u rarr a)(a^(n)-u^(a))/(u^(n)-a^(a))=-1,a>0

Let u_(n)=sum_(k=1)^(n)(k) and v_(n)=sum_(k=1)^(n)(k-0.5) . Then lim_(n rarr oo)(sqrt(u_(n))-sqrt(v_(n))) equals

If u=ax+b, then (d^(n))/(dx^(n))(f(ax+b)) is equal to a.(d^(n))/(du^(n))(f(u)) b.a(d^(n))/(du^(n))(f(u)) c.a^(n)(d^(n))/(du^(n))f(u) d.a^(-n)(d^(n))/(dx^(n))(f(u))

lim_ (u rarr1) (1 + u ^ (1) / (3))) / (1 + u ^ ((1) / (5)))

If U_(n)=(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))^(2).............(1+(n^(2))/(n^(2)))^(n) m then lim_(n to oo)(U_(n))^((-4)/(n^(2))) is equal to

If we assume u = tan^-1 2x , prove that lim_(x rarr 0) x/(tan^-1 2x) = 1/2 lim_(u rarr 0) (tan u)/u

For the sequence {u_(n)} if u_(1) = (1)/(4) and u_(n+1) = (u_(n))/(2+u_(n)) , find the value of (1)/(u_(50)) .

If u_(n)=sin^(n)theta+cos^(n)theta, then prove that (u_(5)-u_(7))/(u_(3)-u_(5))=(u_(3))/(u_(1))

For the sequence {u_(n)} if u_(1) = (1)/(2) and u_(n+1) = (u_(n))/(1+2u_(n))(n ge 1) , find the value of u_(96) .

Let u_(n)=(1)/(sqrt((5)))[((1+sqrt(5))/(2))^(n)-((1-sqrt(5))/(2))^(n)] (0=0,1,2,3,……) , prove that u_(n+1)=u_(n)+u_(n-1)(n ge 1) .