Let `f(x)={cos[x],xgeq0|x|+a ,x<0` The find the value of `a ,` so that `("lim")_(xvec0)` `f(x)` exists, where `[x]` denotes the greatest integer function less than or equal to `x` .

Let f(x)={1+|x|,x<-1[x],xgeq-1 , where [.] denotes the greatest integer function. The find the value of f{f(-2,3)}dot

Let f(x)=cos x sin2x then

Let f(x)=sin x,x =0 then

Let f(x)=cos x sin2x, then

Let f(x)={[x]x in I x-1x in I (where [.] denotes the greatest integer function) and g(x)={sinx+cosx ,x<0 1,xgeq0 . Then for f(g(x))a tx=0 (lim)_(xvec0)f(g(x)) exists but not continuous Continuous but not differentiable at x=0 Differentiable at x=0 (lim)_(xvec0)f(g(x)) does not exist f(x) is continuous but not differentiable

Let f(x)={x^3+x^2+10 x ,\ \ x<0-3sinx ,\ \ \ \ xgeq0 . Investigate x=0 for local maxima/minima.

Let : f(x)={(a+3cosx)/(x^2),x<0btan(pi/([x+3])),xgeq0 If f(x) is continuous at x=0, then find aa n db , where [dot] denotes the greatest integer function.

Let f(x)={x^(2)|(cos)(pi)/(x)|,x!=0 and 0,x=0,x in R then f is

Let F (x) = [{:(cos x , -sin x , 0),(sin x , cos x , 0),(0 , 0, 1):}] , then