If `3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9)` for all `x!=0,` then find the value of `("lim")_(xvec0)f(x)`

If 3-x^(2)/(12) le f(x) le 3+x^(3)/9" for all "x ne 0 , then the value of underset(h to 0)lim f(x) is equal to

If f'(3)=8 then the value of Lt(x → 0)(f(3+x)-f(3-x))/(2x)=

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)={{:(0,x lt 0),(x^(2),xge0):} , then for all values of x

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:R rarr R be a function satisfying Lim_(xrarr0^(+))f(x)=2 , Lim_(xrarr0^(-)) f(x)=3 and f(0)=4 The value of (Lim_(xrarr0) f(x^(3)-x^(2)))/(Lim_(xrarr0) f(2x^(4)-x^(5)))=

If f'(x)=(1)/(1+x^(2)) for all x and f(0)=0 , show that 0.4 lt f (2) lt2

If sqrt(3) sin x - cos x = 0 and 0 lt x lt 90 , find the value of x .

If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the greatest integer function) (lim)_(xvec0^+)f(x)=-1 b. (lim)_(xvec0^-)f(x)=0 c. (lim)_(xvec0^)f(x)=-1 d. (lim)_(xvec0^)f(x)=0