64.0k views
1 vote
Please help. I don't understand what to input into the c...

Please help. I don't understand what to input into the c...-example-1

1 Answer

0 votes

Factorize the denominator:


x^2-31x+240 = (x-16)(x-15)

Then we find that ...

• When c = 15,


\displaystyle \lim_(x\to15)f(x) = \lim_(x\to15)(x-15)/((x-16)(x-15)) = \lim_(x\to15)\frac1{x-16} = \frac1{15-16} = \frac1{-1} = \boxed{-1}

because the factors of x - 15 in the numerator and denominator cancel with each other. More precisely, we're talking about what happens to f(x) as x gets closer to 15, namely when x ≠ 15. Then we use the fact that y/y = 1 if y ≠ 0.

• When c = 16,


\displaystyle \lim_(x\to16)f(x) = \lim_(x\to16)(x-15)/((x-16)(x-15)) = \lim_(x\to16)\frac1{x-16} = \frac10

which is undefined; so this limit does not exist.

• When c = 17,


\displaystyle \lim_(x\to17)f(x) = \lim_(x\to17)(x-15)/((x-16)(x-15)) = \lim_(x\to17)\frac1{x-16} = \frac1{17-16}=\frac11 =\boxed{1}

because the function is continuous at x = 17.

User Christina
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories