find the following limit

Question

lim          x^4 - 7x =12 dived by x-2

x→2

Answer 1

Assume you mean (x⁴-7x-2)/(x-2), which factorises:

(x³+2x²+4x+1)(x-2)/(x-2)=x³+2x²+4x+1 when x≠2. (You can se this if you divide x-2 into x⁴-7x-2.)

But if we are considering x→2, the expression approaches 2³+2(2²)+4(2)+1=25.

If you meant (x⁴-7x-12)/(x-2) or (x⁴-7x+12)/(x-2) the limit would be infinity.