`lim_(x->1)((7+x)^(1/3)-(3+x^2)^(1/2))/(x-1)`

Evaluate lim_(xto1)(root(3)(7+x^3)-sqrt(3+x^2))/(x-1)

If L=lim_(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| is

If L=lim_(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| is

If L=lim_(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| is

lim_(x rarr1)(3sqrt(7+x^(3))-sqrt(3+x^(2)))/(x-1) is equal to

Evaluate the limits : lim_(x to 1) (sqrt(7+x^3)-sqrt(3+5x^2))/(x-1)

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

lim_(x rarr0)((1+x)^((1)/(3))-(1-x)^((1)/(3)))/(x)=(2)/(3)

lim_(x rarr0)((1+x)^((1)/(3))-(1-x)^((1)/(3)))/(x)=(2)/(3)