`F(x)` is the function such that `(lim)_(x->0)(f(x))/x=1\ a n d\ (lim)_(x->0)(x(1+acosx))/((f(x))^3)=1` , then find the value of `a`

Let f(x) be a function such that ("lim")_(xvec0)(f(x))/x=1 and ("lim")_(xvec0)(x(1+acosx)-bsinx)/((f(x))^3)=1 , then b-3a is equal to

If ("lim")_(x->a)[f(x)+g(x)]=2a n d ("lim")_(x->a)[f(x)-g(x)]=1, then find the value of ("lim")_(x->a)f(x)g(x)dot

If the function f(x) satisfies (lim)_(x->1)(f(x)-2)/(x^2-1)=pi, evaluate (lim)_(x->1)f(x)

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

f(x) is the function such that underset( x rarr 0 ) ("Lim") (f(x))/( x ) = 1 . If underset( x rarr 0 ) ( "Lim") ( x ( 1+ a cos x )-b sinx ) /( (f(x))^(3))= 1 , then find the value of a and b.

For the function f(x) = 2 . Find lim_(x to 1) f(x)

For the function f(x) = 2 . Find lim_(x to 1) f(x)

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

If (x^2+x−2)/(x+3) -1) f(x) then find the value of lim_(x->-1) f(x)