Let `f(x)={:abs((x^(3),sinx,cos x),(6,-1,0),(p,p^(2),p^(3))):}`, where p is constant. Then, find `(d^(3))/(dx^(3))[f(x)]` at `x=0`

If f(x)=|{:(x^(3),x^(4),3x^(2)),(1,-6,4),(p,p^(2),p^(3)):}| , where p is a constant, then (d^(3))/(dx^(3))(f(x)) , is

Let f(x)=|[x^3,sinx,cosx],[6,-1, 0],[p, p^2,p^3]| , where p is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is (a) p (b) p-p^3 (c) p+p^3 (d) independent of p

Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is p (b) p-p^3 p+p^3 (d) independent of p

If f(x)=(sin3pix+Asin5pix+Bsinpix)/((x-1)^(5)) for x!=1 is continuous at x=1 and f(x)=(p^(2)pi^(5))/((p+1)) , then evaluate p.

The range of a random variable X is {0, 1, 2}. Given that P(X=0)=3c^(3),P(X=1)=4c-10c^(2),P(X=2)=5c-1 where c is constant. Find (i) the value of c (ii) P(X lt 1) (iii) P(1lt X le2) (iv) P(0lt X le3)

Let P_(n)=a^(P_(n-1))-1,AA n=2,3,..., and let P_(1)=a^(x)-1, where ainR^(+). Then evaluate lim_(xto0) (P_(n))/(x).

If f(x)={{:((1+|sinx|)^((p)/(|sinx|)),",",-(pi)/(6)ltxlt0),(q,":",x=0),(e^(tan3x.cot5x),":",0ltxlt(pi)/(6)):} is continuous at x = 0, then the value of 2p+10lnq is equal to

If f(x)=(2x+3sinx)/(3x+2sinx),x!=0 is continuous at x=0 , then find f(0)dot

If f(x)=(2x+3sinx)/(3x+2sinx) , x!=0 is continuous at x=0 , then find f(0)

If f(x)={{:(x^(p+1)cos.(1)/(x)":", x ne 0),(0":", x=0):} then at x = 0 the function f(x) is