Evaluate the value of `("lim")_(n vec pi/2 )tan^2xsqrt((2sin^2x+3sinx+4)-sqrt(sin^2x+6sinx+2))`

Evaluate lim_(xto pi//2) tan^(2)x[sqrt(2sin^(2)x+3sinx+4)-sqrt(sin^(2)x+6sinx+2)]

intcosx/sqrt(sin^2x+3sinx+4)dx

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

The value of lim_(xto pi//4)((cosx+sinx)^(3)-2sqrt(2))/(1-sin2x) is

int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=

Evaluate the following limit: (lim)_(x->pi/4)(1-t a n x)/(1-sqrt(2)sinx)

Find the value of lim_(xto0) (sinx+log_(e)(sqrt(1+sin^(2)x)-sinx))/(sin^(3)x).

Find the range of f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1)

Find the range of f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1)

lim_(x->0)(x+2sinx)/(sqrt(x^2+2sinx+1)-sqrt(sin^2x-x+1))