Evaluate: `lim_(x->oo) (1+1/(a+bx))^(c+dx)` , where `a,b,c` and dare positive

Evaluate: lim_(x->oo)[x(a^(1/x)-1)], a >1

Evaluate: lim_(x->oo) (x+7sinx)/(-2x+13)

Evaluate: lim_(n->oo)(4^n+5^n)^(1/n)

Evaluate the limit: lim_(x->oo)((x+2)/(x+1))^(x+3)

Evaluate : lim_(x->oo)(a x^2+b x+c)/(dx^2+e x+f)dot

Solve: lim_(x->oo)2^(x-1) tan(a/(2^x))

If the magnitude of the coefficient of x^(7) in the expansion of (ax^(2)+(1)/(bx))^(8) , where a, b are positive numbers, is equal to the magnitude of the coefficient of x^(-7) in the expansion of (ax-(1)/(bx^(2)))^(8) , then a and b are connected by the relation

lim _( x to oo) (1+ (1)/(x))^(x//2) is equal to-

Evaluate: lim_(x->oo)x(tan^(-1)((x+1)/(x+4))-pi/4)

Evaluate: lim_(x->oo)(sqrt(3x^2-1)-sqrt(2x^2-1))/(4x+3)