Find a value of the constant k such that the limit exists.(adsbygoogle = window.adsbygoogle || []).push({});

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

^{x->1}

We could do...

just try number until it factors nicely..

k would equal 5.. to give us

x^{2}-5x+4 = (x-1)(x-4)

the (x-1) would cancel .. leaving just x-4.. and the limit would be 1-4 = -3...

Is there an easier way of doing this than just guessing to try to figure out which value of k would make the polynomial factor nicely so that it would cancel with the factor in the denominator? Because, some of the other problems in this section get a little too tough to just be able to spit out the answer...

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# Homework Help: Find a value of the constant k such that the limit exists

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