असमिका `।x। gt 0` का हल `x in R - {0}` है ।

1/(2x-1)gt0, x in R

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then (a) P(x) gt 0 for all x in R and Q(x) lt 0 for all x in R . (b) P(x) lt 0 for all x in R and Q(x) gt 0 for all x in R . (c) neither P(x) gt 0 for all x in R nor Q(x) gt 0 for all x in R . (d) exactly one of P(x) or Q(x) is positive for all real x.

Given that f(x) gt g(x) for all x in R and f(0) =g(0) then

Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R . Then for all x

If f(x) is a quadratic expression such that f(x)gt 0 AA x in R , and if g(x)=f(x)+f'(x)+f''(x) , then prove that g(x)gt 0 AA x in R .

If f(x) is a quadratic expression such that f(x)gt 0 AA x in R , and if g(x)=f(x)+f'(x)+f''(x) , then prove that g(x)gt 0 AA x in R .

If f: R to R defined by f(x) ={{:(2x+5, if, x gt 0),(3x-2, if, x le 0):} then f is

Show that the Signum Function f: R to R, given by f (x) ={{:(1, if x gt 0), ( 0, if x =0),(-1, if x lt0):} is neither one-one nor onto.

Show that the signum function f : R rarr R given by f(x)= {(1,if x gt 0), (0, if x = 0), (-1, if x lt 0) :} is neither one-one nor onto.

Show that the signum function f : R to R given by: f(x) = {{:(1, if x gt 0),(0, if x =0),(-1, if x lt 0):} is neither one-one nor onto.