Need help in determining the lim

[Equilibrium]

Hi

$$\lim_{x\rightarrow 4}\frac{x^2 - 3x + 4}{2x^2 - x - 1}$$

this is lim x ->4 which is the cube root of the whole fraction ^

Is there any way to answer this because i can't really factor it...

 

[courtrigrad]

Why not just evaluate the limit at $x = 4$?

 

[dextercioby]

You don't need to factor it. It can easily be factored, since it's a ratio of quadratic polynomials.

Daniel.

 

[dontdisturbmycircles]

Assuming f(x) is continuous at f(a) ($$\lim_{x \rightarrow a^{+}} f(x) = f(a) =\lim_{x \rightarrow a^{-}} f(x)$$) you can always just plug in a. The only time you would need to factor is if f(x) is not continuous at a or if plugging in a would result in an undefined function (0 in denominator). So yea, as courtigrad said, just substitute x=4. :-)