If `f(x)=sum_(lambda=1)^n(x-5/lambda)(x-4/(lambda+1)),` then `lim_(n rarr oo)f(0)` is equal to

If f(x)=|(x,lambda),(2lambda,x)| , then f(lambdax)-f(x) is equal to

lim_(x rarr oo)((x+lambda)/(x-lambda))^(x)=4 then lambda

lim_(x rarr5)(x^(lambda)-5^(lambda))/(x-5)

lim_(x->pi)(2-lambda/x)^(2tan((pipi)/(2lambda)))=1/e, then lambda is equal to -

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) then 4(lim_(x rarr oo)sum_(x-1)^(n)(1)/(T_(r))) is equal to

lim_(lambda rarr0)(int_(0)^(1)(1+x)^(lambda)dx)^((1)/(lambda)) is equal to

lim_(x rarr1)sec^(-1)((lambda^(2))/(ln x)-(lambda^(2))/(x-1)) exists then lambda belong to

If alpha in(0,1) and f:R rarr R and lim_(x rarr oo)f(x)=0,lim_(x rarr oo)(f(x)-f(alpha x))/(x)=0 then lim_(x rarr oo)(f(x))/(x)=lambda where 2 lambda+7 is