Evaluate the limit:lim𝑥→5𝑥2+𝑥−30𝑥2−7𝑥+10=

To evaluate the limit of the given function as x approaches 5, we can simply substitute x = 5 into the function. However, before we do that, we need to simplify the function.

The function is a rational function and it can be simplified by factoring the numerator and the denominator.

The numerator x^2 + x - 30 can be factored into (x - 5)(x + 6). The denominator x^2 - 7x + 10 can be factored into (x - 5)(x - 2).

So, the function becomes (x - 5)(x + 6) / (x - 5)(x - 2).

We can cancel out the common factor (x - 5) from the numerator and the denominator.

This gives us a new function: (x + 6) / (x - 2).

Now, we can substitute x = 5 into this new function to find the limit as x approaches 5.

lim (x→5) (x + 6) / (x - 2) = (5 + 6) / (5 - 2) = 11 / 3.

So, the limit of the given function as x approaches 5 is 11/3.