[*4(sqrt(1+x)-1)/(x)=],[x+0],[" (a) "0]

If f(x) is continuous at x=0 , where f(x)={((sin x)/(x)+cos x", for " x gt 0),((4(1-sqrt(1-x)))/(x)", for " x lt 0):} , then f(0)=

The limit of [(1)/(x)sqrt(1+x)-sqrt(1+(1)/(x^(2))]] as x rarr0

Discuss the continuity of f(x) = 0 at x = 0 if f(x) = {{:((sqrt(1 + 4x)- sqrt(1 - 4x))/(sin x)"," ,x != 0),(4, x = 0):}

If tan^(-1)(sqrt(1+x^(2))-1)/x=4^(0) , then

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

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

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) = (x)/(2), x in (0, (pi)/(4))

Prove that: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x in(0,(pi)/(4))

Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) = (x)/(2), x in (0, (pi)/(4))