`d/(dx)[lim_(x rarr a)(x^5-a^5)/(x-a)]=`

Which of the following true ({.} denotes the fractional part of the function)? lim_(x rarr oo)(log_(e)x)/({x})=oo( b) lim_(x rarr2^(+))(x)/(x^(2)-x-2)=oolim_(x rarr1^(-))(x)/(x^(2)-x-2)=-oo( d) lim_(x rarr oo)(log_(0)5x)/({x})=oo

lim_(x rarr 0) ((1 + 2x)^(10) - 1)/(x) is equal to a)5 b)10 c)15 d)20

lim_(x rarr0)(a^(x)-b^(x))/(c^(x)-d^(x))

let a=lim_(x rarr1)((x)/(ln x)-(1)/(x ln x)),b=lim_(x rarr0)((x^(3)-16x)/(4x+x^(2))),c=lim_(x rarr0)(ln(1+sin x))/(x) and d=lim_(x rarr-1)((x+1)^(3))/(3[sin(x+1)-(x+1)]) then the matrix [[a,bc,d]]

Which of the following is/are true? (a) lim_(x rarr oo)((2+x)^(40)(4+x)^(5))/((2-x)^(45))=1(b)lim_(x rarr0)(1-cos^(3)x)/(x sin x cos x)=(3)/(2)(c)lim_(x rarr0)(ln(1+2x)-2ln(1+x))/(cot^(-1)(sqrt(x+1)-sqrt(x)))=-1 (d) lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^(1)((2x+1)/((x-1)^(2)))=1)=-1 (d)

If p= lim_(x rarr0^(+))[(3sin x)/(x)] ,q= lim_(x rarr0^(+))[(3x)/(sin x)] ,r= lim_(x rarr0^(+))[(tan x)/(x)] and s=lim_(x rarr0^(+))[(3tan x)/(x)] where [.] denotes the greatest integer function (A) pqrs=18 (B) pqrs=0 (C) p+q+r+s=9 (D) pq+rs+qr+sp=18

For x in R,lim_(x rarr oo)((x-3)/(x+2))^(x) is equal to (a) e (b) e^(-1)(c)e^(-5)(d)e^(5)

If f(x) is differentiable and strictly increasing function,then the value of lim_(x rarr0)(f(x^(2))-f(x))/(f(x)-f(0)) is 1 (b) 0(c)-1 (d) 2

D*f(x)=lim_(h rarr0)(f^(2)(x+h)-f^(2)(x))/(h) If f(x)=x ln x then D*f(x) at x=e equals

the value of lim_(x rarr3^(+))(|x-3|)/(x-3)(a)1(b)-1(c)0(d)oo