6) `lim_(x->0)(1+3x^2)/(x)`

value of lim_(x->0)(1-cos^3x)/(xsinx*cosx) is

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

Evaluate lim_(x->0^-) (x^2-3x+2)/(x^3-2x^2)

lim_(x->0)(1/(x^2)-1/(tan^2x))

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

Evaluate lim_(x-> 0) (tan3x-2x)/(3x- sin^2 x)

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

If lim_(x->0)(1+a x+b x^2)^(2/x)=e^3, then find the value of a and b.

Evaluate: lim_(x->0) (1-cos2x)/(x^2)

find lim_(x->1) ((x^4-3x^2+2)/(x^3-5x^2+3x+1))