Show that `underset(xrarrpi//2)Lt[sinx]=0`, where [x] stands for the integral part of x.

How many real solutions of the equation 6x^(2)-77[x]+147=0 , where [x] is the integral part of x ?

Prove that f (x) =x-[x], where [x] denotes the integral part of x not exceeding and is periodic and find its period.

underset(xrarrpi/2)lim (1-sinx)/(cosx) is equal to:

underset(xrarrpi/2)lim (secx-tanx) is equal to:

Show that the equation x^(3)+2x^(2)+x+5=0 has only one real root, such that [alpha]=-3 , where [x] denotes the integral point of x

Evaluate the following integrals: underset(0)overset(1.5)int[x] dx, where [x] is greatest integer function.

underset(xrarr0)lim (sinx)/x is equal to:

Find the period f(x)=sinx+{x}, where {x} is the fractional part of xdot

underset(xrarrpi/4)lim (sec^2x-2)/(tanx-1) is equal to:

If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","for",x lt -1):} , where [x] denotes the integral part of x, then for what values of a, b, the function is continuous at x = - 1?