Discuss the continuity of `f(x)={x{x}+1,0lt=x<1 and 2-{x},1lt=x<2` where `{x}` denotes the fractional part function.

Discuss the extremum of f(x)={|x^2-2|, -1lt=x

Discuss the extremum of f(x)=sinx+1/2sin2x+1/3sin3x ,0lt=xlt=pidot

f(x)={[sinpix],0lt=x<1sgn(x-5/4)x{x-2/3},1lt=xlt=2 where [.] denotes the greatest integer function and {.} represents the fractional part function. At what points should the continuity be checked? Hence, find the points of discontinuity.

Let f(x)={1+(2x)/a ,0lt=x<1 and ax ,1lt=x<2 If lim_(x->1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

If f(x)={x+1/2, x<0 2x+3/4,x >=0 , then [(lim)_(x->0)f(x)]= (where [.] denotes the greatest integer function)

If X is the random variable with porbability density function f(x) given by f(x)={(x-1,1lt=xlt2),(-x+3,2lt=xlt3),(0,"otherwise"):} find (i) the distribution function F(x) (ii) P (1.5lt=X lt=2.5)

If X is the random variable with distribution function F(x) given by , F(x) = {(o,xlt0),(x,0lt=xlt1),(1,1lt=x):} then find (i) the probability density function f(x) (ii) P(0.2lt=Xlt=0.7) .

Draw the graph of f(x) = [log_(e)x], e^(-2) lt x lt 10 , where [*] represents the greatest integer function.

The number of point f(x) ={{:([ cos pix],0le x lt1),( |2x-3|[x-2],1lt xle2):} is discontinuous at Is ([.] denotes the greatest intgreal function )

Find the equivalent definition of f(x)=max{x^2,(1-x)^2,2x(1-x)} where 0lt=xlt=1