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

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]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),xgeq0, be a non-negative continuous function, and let f(x)=int_0^xf(t)dt ,xgeq0, if for some c >0,f(x)lt=cF(x) for all xgeq0, then show that f(x)=0 for all xgeq0.

Let f(x),xgeq0, be a non-negative continuous function, and let F(x)=int_0^xf(t)dt ,xgeq0, if for some c >0,f(x)lt=cF(x) for all xgeq0, then show that f(x)=0 for all xgeq0.

Let f(x) = {-x^2 ,for x<0x^2+8 ,for xgeq0 Find x intercept of tangent to f(x) at x =0 .

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

Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)cosxlt=f(x)sinxAAxgeq0, then find f((5pi)/3)

Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)cosxlt=f(x)sinxAAxgeq0, then find f((5pi)/3)

Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)cosxlt=f(x)sinxAAxgeq0, then find f((5pi)/3)