`(lim)_(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x))/b)` has the value equal to `(a-b)/3` b. 0 c. `((a^2-b^2))/(6a^2b^2)` d.`` `(a^2-b^2)/(3a^2b^2)`

lim_(x rarr0^(+))(1)/(x sqrt(x))(atan^(-1)(sqrt(x))/(a)-b tan^(-1)(sqrt(x))/(b)) has the value equal to (a-b)/(3) b.0 c.((a^(2)-b^(2)))/(6a^(2)b^(2)) d.(a^(2)-b^(2))/(3a^(2)b^(2))

(lim)_(xvec0)((sqrt(1+x s in x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c.3 d. 2

The value of the limit ("lim")_(xvec0)(a^(sqrt(x))-a^(1sqrt(x)))/(a^(sqrt(x))+a^(1sqrt(x))),a >1,i s (a) 4 (b) 2 (c) -1 (d) 0

(lim)_(x->0)(sqrt(1+x)-1)/x is equal to a. 1 b . 0 c. 2 d. 1/2

(lim)_(xvec0)((sqrt(1+x sin x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c. 3 d. 2

(lim)_(xvec0)((sqrt(1+x sin x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c. 3 d. 2

(lim)_(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 c. 2 d. e^2

(lim)_(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 c. 2 d. e^2

The value of the limit ("lim")_(xvec0)(a^(sqrt(x))-a^(1sqrt(x)))/(a^(sqrt(x))+a^(1sqrt(x))),a >1,i s 4 (b) 2 (c) -1 (d) 0

If int_(0)^(b)(1)/(sqrt(1+x)-sqrt(x))dx=(2)/(3)(2sqrt(2)) , then b =