172k views
1 vote
Determine the value of k for which f(x) is continuous.

Determine the value of k for which f(x) is continuous.-example-1

1 Answer

3 votes

These are the conditions of the continuity in a function:

First, the value of x must have an image.

Second, the lateral limits must be equal:


\lim_(x\to a^+)f(x)=\lim_(x\to a^-)f(x)

Finally, the value of the limit must be equal to the image of x. This means that:


f(a)=\lim_(x\to a^)f(x)

In this case, we must find a value of k that can make the two lateral limits equal in x =3:


\lim_(x\to3^+)x^2+k=\lim_(x\to3^-)kx+5

We can solve these two limits easily by replacing the x with the value of 3


3^2+k=3k+5
\begin{gathered} 9+k=3k+5 \\ 4=2k \\ k=2 \end{gathered}

Finally, we can see that the answer is k=2.

User ElGeekalpha
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