Finding k for x is undefined at $x=2$

  • MHB
  • Thread starter karush
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In summary, when "k" is undefined at x=2, it means that there is no value of "k" that can make the expression for x equal to 2. It is important to find the value of "k" for x=2 because it helps us understand the behavior of the expression at that point. To find the value of "k" for x=2, we need additional information such as an equation or a graph. "k" can be either a complex number or a real number, depending on the expression for x. Finally, the value of "k" can greatly affect the behavior of the expression at x=2, determining things like continuity, complex roots, and asymptotes.
  • #1
karush
Gold Member
MHB
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5
If $f(x)=\begin{cases}
\dfrac{(2x+1)(x-2)}{x-2}, &\text{for } x\ne 2 \\[3pt] k, &\text{for } x=2 \\
\end{cases}$
for what number k will the function be continuous
a. 0 b. 1 c. 2 d. 3 e. 5
---------------------------------
I chose
[e] x is undefined at $x=2$ so
rewrite as $2x+1$
plug in $f(2)=2(2)+1=5=k$

hopefully
probably suggestions etc
 
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  • #2
for f(x) to be continuous at x = 2 ...

$\displaystyle \lim_{x \to 2} f(x) = f(2)$
 
  • #3
So discontinuous. Means a hole always?
 
  • #4
karush said:
So discontinuous. Means a hole always?

not just a hole (a removable discontinuity)

also, a vertical asymptote or a jump (non-removable discontinuities)
 

Related to Finding k for x is undefined at $x=2$

1. What does it mean for k to be undefined at x=2?

When we say that k is undefined at x=2, it means that the value of k cannot be determined or does not exist when x is equal to 2. This could be due to a mathematical limitation or a specific condition that makes it impossible to find a value for k at x=2.

2. How do you find the value of k when x=2 is undefined?

If x=2 is undefined for k, it means that the equation or function involving k and x does not have a solution at this specific value. In this case, we cannot find the value of k when x=2. However, we can still find the value of k for other values of x.

3. Can we use a different value for x to find k when x=2 is undefined?

Yes, we can use a different value for x to find k. When x=2 is undefined, it means that the equation or function does not have a solution at this specific value. However, we can still use other values of x to find the value of k.

4. What could cause k to be undefined at x=2?

There could be various reasons for k to be undefined at x=2. It could be due to a mathematical limitation, such as a division by zero, or a specific condition in the equation or function that makes it impossible to find a solution at x=2.

5. Is it possible for k to be undefined at values other than x=2?

Yes, it is possible for k to be undefined at values other than x=2. The value of k can be undefined at any value of x where the equation or function does not have a solution. This could be a specific value or a range of values depending on the equation or function.

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