if for all real value of `x,(4x^2+1)/(64x^2-96x.sina+5)<1/32`,then a lies in the interval

if for all real value of x,(4x^(2)+1)/(64x^(2)-96x.sin a+5)<(1)/(32) ,then a lies in the interval

For all real values of x if |(x^(2)-3x-1)/(x^(2)+x+1)|<3 limit of x are

If x is real , show that each of the following expressions is capable of assuming all real values: (2x^2+4x+1)/(x^2+4x+2)

If ((x-5)(x^2-2x+1))/((x-7)(x^2+2x+3)) is positive for all real values of x, show that x has no value between 5 and 7.

Find all the real values of x for which (x-1)/(4x+5)lt(x-3)/(4x-3)

Find the domain of the real-valued function: f(x)=(x^(2)-x+1)/(x^(2)-5x+4) .

If (x^2+a x+3)//(x^2+x+a) takes all real values for possible real values of x , then a. 4a^2+39 -0 c. ageq1/4 d. a<1/4

For all real values of x, the maximum value of (1-x+x^(2))/(1+x+x^(2)) is :

If (x^(2)+ax+3)/(x^(2)+x+a) takes all real values for possible real values of x, then a.4a^(2)+39 0 c.a>=(1)/(4) d.a<(1)/(4)