" (vii) `f(x)=3x^(2)-1;x=(1)/(sqrt(3)),(2)/(sqrt(3))`

int(1)/(sqrt(3x+2)+sqrt(3x+1))

y = tan ^ (- 1) [(3x-x ^ (3)) / (1-3x ^ (2))], - (1) / (sqrt (3))

f(x)=(x-1)|(x-2)(x-3)|* Then f decreases in (a) (2-(1)/(sqrt(3)),2) (b) (2,2+(1)/(sqrt(3)))(c)(2+(1)/(sqrt(3)),4) (d) (3,oo)

int_(th x^(2)(x))^( If )((x+2)dx)/((x^(2)+3x+3)sqrt((x+1)))=(2)/(sqrt(3))[tan^(-1)((f(x)+1)/(sqrt(3)))+tan^(-1)((f(x)-1)/(sqrt(3)))]+c

The domain and range of real function f if (i) f(x)=sqrt(1-x^(2))(ii)sqrt((x-1)(x-3))(iii)sqrt(4x-x^(2)-3)

Solution of (2+sqrt(3))^(x^(2)-2x+1)+(2-sqrt(3))^(x^(2)-2x-1)=(4)/(2-sqrt(3))are(A)1+-sqrt(3),1(B)1+-sqrt(2),1(C)1+-sqrt(3),2(D)1+-sqrt(2),2

Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1))-ln x in [(1)/(sqrt(3)), sqrt(3)] .

Find the domain of the real valued function f(x)=sqrt(x^(2)-1)+(1)/(sqrt(x^(2)-3x+2))

If mean value theorem holds good for the function f(x)=(x-1)/(x) on the interval [1,3] then the value of 'c' is 2 (b) (1)/(sqrt(3))( c) (2)/(sqrt(3))(d)sqrt(3)

If tan^(-1)x+2cot^(-1)x=(2 pi)/(3), then x, is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3)(d)sqrt(2)