Consider the determinant
`f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2)+c),(x^(4)+b,x-c,0):}|`
Statement -1 `f(x) =0` has one root `x =0`.
Statement -2 The value of skew -symmetric determinant of odd order is always zero.

If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}| , then "............"

If ane0,bne0,cne0 and |{:(0,x^2+a,x^4+b),(x^2-a,0,x-c),(x^3-b,x^2+c,0):}|=? , for x=0

Let f(x) =|{:(secx,x^(2),x),(2sinx,x^(3),2x^(2)),(tan3x,x^(2),x):}|lim_(x to 0)f(x)/(x^(4)) is equal to

If a,b,c are in A.P then the determinant |{:(x+2,x+3,x+2a),(x+3,x+4,x+2b),(x+4,x+5,x+2c):}| is …..

If f'(x)=3x^(2)-(2)/(x^(3)) and f(1)=0 then find f(x).

|{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}|=0 where a,b,c are in A.P

Consider the polynomial function f(x)=x^7/7-x^6/6+x^5/5-x^4/4+x^3/3-x^2/2+x Statement-1: The equation f(x) = 0 can not have two or more roots.Statement-2: Rolles theorem is not applicable for y=f(x) on any interval [a, b] where a,b in R

Consider f(x) = {{:((8^(x) - 4^(x) - 2^(x) + 1)/(x^(2))",",x gt 0),(e^(x)sin x + pi x + k log 4",",x lt 0):} Then, f(0) so that f(x) is continuous at x = 0,then k=

f(x)= {((x(1 + a cos x)-b sin x)/(x^(3))",",x ne 0),(0",",x=0):} . If f is continuous at x=0 then find the value of a and b.

If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} then f(x) is