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

The value of lim_(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2 c. e^(-2) d. 1

lim_(x->0)(e^(5x) - 1)/(3x)

the value of lim_(x->0){(cosx)^(1/(sin^2x))+(sin2x+2tan^-13x+3x^2)/(ln(1+3x+sin^2x)+xe^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

Let a= lim_(x->0)ln(cos2x)/(3x^2), b=lim_(x->0)(sin^(2)2x)/(x(1-e^x)), c=lim_(x->1)(sqrt(x)-x)/lnx

The value of lim_(x to oo)((1+3x)/(2+3x))^((1-sqrt(x))/(1-x)) is

Evaluate lim_(xto0)((1+5x^(2))/(1+3x^(2)))^(1//x^(2))

Evaluate the following limits : Lim_(x to 1)(1-x^(-1//3))/(1-x^(-2//3))

The value of lim_(xto oo)(2x^(1//2)+3x^(1//3)+4x^(1//4)+....nx^(1//n))/((2x-3)^(1//2)+(2x-3)^(1//3)+....+(2x-3)^(1//n)) is

The value of lim_(xto oo)(2x^(1//2)+3x^(1//3)+4x^(1//4)+....nx^(1//n))/((2x-3)^(1//2)+(2x-3)^(1//3)+....+(2x-3)^(1//n)) is