Question

Find k for which the limit below exists, and find the limit.

lim x->1 (2x^2 + kx +4)/(x-1)

Please show me how to do both procedures. Thanks

Answer 1

well, if the limit exists, then in the numerator you have to have (x-1).

so if (2+k+4) is approaching zero, then
k=-6

lim x>1 (2x^2-6x+4)/(x-1)= lim 2(x^2-3x+2)/(x-1)=lim 2(x-1)(x-2)/(x-1)=
lim x>1 (2(x-2))=2*-1=-2
check that