`(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)_(x->0)((sqrt(1+xsin x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c. 3 d. 2

lim_(x to 0) (sqrt(1 + x + x^(2)) - sqrt(x + 1))/(2X^(2)) is equal to

Evaluate the limit: ("lim")_(xvec0)(sqrt(2)-sqrt(1+cosx))/(sin^2x)

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

lim _(xto0) (""^(3)sqrt(1+sin ^(2)x )- ""^(4) sqrt(1-2 tan x))/(sin x+ tan ^(2) x) is equal to:

(lim)_(xvec0)(l"n"(1+2x)-2"ln"(1+x))/(x^2) is equal to 3 b. 1 c. -1 d. 0

("lim")_(xvec0)(5sinx-7sin2x+3sin3x)/(x^2sinx)

(lim)_(xvec0)(1-cos^3x)/(x s i n x cos x) is equal to 3 b. 1/2 c. 3/2 d. -3/2

(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")_(xvec0)("cos"(tanx)-cosx)/(x^4)i se q u a lto 1/6 (b) -1/3 (c) 1/2 (d) 1