If `f(x)=sin^(-1)x` then prove that `lim_(x->1/2)f(3x-4x^3)=pi-3lim_(x->1/2)sin^(-1)x`

If f(x)=sin^(-1)x then prove that lim_(x rarr(1)/(2))f(3x-4x^(3))=pi-3lim_(x rarr(1)/(2))sin^(-1)x

If f(x) = sin^(-1) x then prove that lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x

If f(x) = sin^(-1) x then prove that lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x

If f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x) , then [a] is equal to {where [] denotes G.I.F}

If f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x) , then [a] is equal to {where [] denotes G.I.F}

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

If (x^2+x−2)/(x+3) -1) f(x) then find the value of lim_(x->-1) f(x)

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

Which of the following is/are true? (a) lim_(x->oo)((2+x)^(40)(4+x)^5)/((2-x)^(45))=1 (b) lim_(x->0)(1-cos^3x)/(xsinxcosx)=3/2 (c) lim_(x->0)(ln(1+2x)-2"ln"(1+x))/(x^2)=-1 (d) lim_(x->oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^1((2x+1)/(x-1)^2)=1