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4xle21 when x in Z...

`4xle21` when ` x in Z`

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{5,4,3,2,1,0,-1,-2,…}
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4xle21 when x in N

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If the polynomial f(x) be defined by f(x) = {{:(2x^(2)-3 " when " xle2),(2x+1 " when "2ltxle4),(1/(2x-1) "when "xgt4):} then find (a)f(sqrt2),(b)f(pi) .

A function f (x) is defined as follwos : f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):} Examine whether underset(xrarr1)"lim"f(x) exists or not.

If (x+y) prop z when y is constant and (z+x) prop y when z is constant . Then prove that (x+y+z) prop yz , when when y and z are both constant.

Solving graphically show that the following LPP has an infinite number of optimal solution Minimize Z= x+y 5x+9y le 45 x+yge2 xle 4 and x ge 0, y ge 0 Find also the minimum value of the object function Z