" 2."f(x)={[x^(10)-1,," if "x<=1],[x^(2),," if "x>1]

f(x)= {(x^(10)-1",","if" x le 1),(x^(2)",","if" x gt 1):}

Find all points of discontinuity of f, where f is defined by f(x)={x^(10)-1, if""""xlt=1x^2, if""""x >1

Verify the Lagrange's theorem for the following functions: (a) f(x) = x^(3) in [-1,1] (b) f(x) = sin x in [0,pi/2] ( c) f(x) = x^(n) in [-1,1], n in Z^(+) ( d) f(x) =2x^(2) - 7x + 10, x in [2,5]

Suppose f:R rarr R is a function given by f(x)={1e^(x^((10)-1))+(x-1)^(2)sin((1)/(x-1)) if x=1, if x!=1

Test the continuity of f(x), where f(x)={x^(2)+x+1,0<=x<=1 and x^(2)+2,1

If f(x)={x^(2)+1,0<=x<1,-3x+5,1<=x<=2

f(x)={[(1)/(e^(x-1)),,x!=10,,x=1

f(x){{:(10^(3) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}