`f(x)={cos(pix)/2,x >0x+a ,xlt=0` Find the values of `a` if `x=0` is a point of maxima.

f(x)={cos(pix)/2,x >0 x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

Iff(x)={s i^(-1)(sinx),x >0pi/2,x=0,t h e ncos^(-1)(cosx),x<0 x=0 is a point of maxima x=0 is a point of minima x=0 is a point of intersection non eoft h e s e

Let f(x)={{:(cos[x]", "xle0),(|x|+a", "xlt0):}. Then find the value of a, so that lim_(xto0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x.

The curve f(x)=(x^2+a x+6)/(x-10) has a stationary point at (4,1) . Find the values of aa n db . Also, show that f(x) has point of maxima at this point.

" Let " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f(0) and f' (pi//2) .

The probability density function of X is given by f(x) = {(ke^(-x/3),"for" " "xgt0),(0, "for" " " xlt=0):} Find (i) the value of k (ii) the distribution function (iii) P(X lt 3) (iv) P(5lt=X) (v) P(X lt=4) .

If f(x) ={{:(x+2,xlt0),(-x^(2)-2,0le xlt1),( x, xge1):} then the number of points of discontinuity of |f(x)|is

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

If the function f is defined as f(x) = {(3x-2,xgt3),(x^(3)-2,-2lt=xlt=2),(2x+1,xlt-2):} Then find the values, if exists f (4), f (-4), f(0), f(-7).

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n d6x+5x^2,x >0 Then at x=0,f(x) has a local maximum has a local minimum is discontinuous (d) none of these