`lim_(x-gt0)(2^x-1)/x`

lim_(x-gt0) (e^(3x)-1)/(log(1+5x))

lim_(x-gt0)(cos2x-cos3x)/(cos4x-1)

lim_(x-gt0) (xcot4x)/((cot^2 2x)(sin^2 x)) is equal to (A) 1 (B) 2 (C) 4 (D) 6

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

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

Evaluate the limits, if exist lim_(x-gt0)(log_e(1+2x))/(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

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->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->1/2)f(3x-4x^3)=pi-3lim_(x->1/2)sin^(-1)x