If `f(x)={x/(s in x),x >0 2-x ,xlt=0` and `g(x)={x+3,x<1x^2-2x-2,1lt=x<2x-5,xgeq2` Then the value of `(lim)_(xvec0)g(f(x))` a. is -2 b. is -3 c. is 1 d. does not exist

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

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

If f(x)={x-1,xgeq1 2x^2-2,x 0-x^2+1, xlt=0,and h(x)=|x| ,t h e n("lim")_(xvec0)f(g(h(x))) is___

If f(x)={(sin(x^(2)-3x),xle0 .^x+5x^(2),xgt0

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

Let f(x)={{:(x+1", "xlgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):} Find the LHL and RHL of g(f(x)) at x=0 and, hence, find lim_(xto0) g(f(x)).

: If f(x)={x^2+2,xgeq2 1-x ,x 1, 3-x , xlt=0,t h e nt h ev a l u eoflim_(x->1)f(g(x))i s__

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

Which of the following function is not differentiable at x=0? f(x)=min{x ,sinx} f(x)={0,xgeq0x^2,x<0 f(x)= x^2 sgn(x)

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