217 AP Calculus Exam continous function with k

In summary, the 217 AP Calculus Exam consists of two sections: a multiple-choice section and a free-response section. A continuous function is defined as a function with no abrupt jumps or gaps, and the constant k in a continuous function represents the slope or derivative of the function. The continuity of a function is determined by three conditions, and to prepare for the 217 AP Calculus Exam on continuous functions with k, it is important to review relevant material and practice problems.
  • #1
karush
Gold Member
MHB
3,269
5
217

$f(x)=\begin{cases}
\dfrac{(2x+1)(x-2)}{x-2}, &\text{for } x\ne 2 \\[3pt]
k, &\text{for } x=2 \\
\end{cases}$$(A)\,0\quad(B)\,1\quad(C)\,2\quad(D)\,3\quad(E)\,5\quad$

ok not sure if this the standard way to do this but
$x-2$ will cancel out
then if $x=2$ for $2(2)+1 = 5$ which is (E)
 
Last edited:
Physics news on Phys.org
  • #2
Re: 217 AP Caluclus Exam continuous function with k

A function $f(x)$ is continuous at $x=c$ if ...

1. $f(c)$ is defined.

2. \(\displaystyle \lim_{x \to c} f(x)\) exists.

3. \(\displaystyle \lim_{x \to c} f(x)= f(c)\)$f(2) = k$ is defined

\(\displaystyle \lim_{x \to 2} f(x) = 2x+1\) exists.

\(\displaystyle \lim_{x \to 2} f(x) = 2(2)+1 = 5 = k\)
 
  • #3
Thanks I'll add that to the MeWe post
 

Related to 217 AP Calculus Exam continous function with k

1. What is the format of the AP Calculus Exam?

The AP Calculus Exam consists of two sections: a multiple-choice section and a free-response section. The multiple-choice section contains 45 questions and is 1 hour and 45 minutes long. The free-response section contains 6 questions and is 1 hour and 30 minutes long.

2. What topics are covered on the AP Calculus Exam?

The AP Calculus Exam covers a variety of topics including limits, derivatives, integrals, and applications of these concepts. It also includes topics such as continuity, differentiability, and the Fundamental Theorem of Calculus.

3. What is a continuous function?

A continuous function is a function that has no abrupt changes or breaks in its graph. This means that the function is defined and has a value at every point on its domain. In other words, the graph of a continuous function can be drawn without lifting the pencil off the paper.

4. How is the concept of continuity related to the AP Calculus Exam?

The concept of continuity is an important topic in calculus and is often tested on the AP Calculus Exam. It is used to determine if a function is differentiable and to evaluate limits and integrals. Understanding continuity is essential for success on the exam.

5. What is the significance of the constant "k" in a continuous function?

The constant "k" in a continuous function represents the y-coordinate of the point where the function intersects the y-axis. It is also known as the y-intercept. In calculus, the value of "k" can be used to determine the behavior of a function and its derivatives at that point.

Similar threads

Replies
1
Views
1K
Replies
4
Views
1K
  • Calculus
Replies
4
Views
2K
Replies
3
Views
759
  • Calculus
Replies
3
Views
787
  • Calculus
Replies
5
Views
1K
  • Calculus
Replies
4
Views
2K
  • Calculus
Replies
1
Views
1K
  • Calculus
Replies
1
Views
1K
Replies
1
Views
843
Back
Top