1.4.203 AP calculus practice question on Limits

• MHB
• karush
In summary, the conversation is about finding the limit of a function and applying L'Hopital's Rule to solve it. The solution is given as $-\dfrac{1}{2\pi}$ and it is suggested to check for any typos or suggestions. No further information is provided.
karush
Gold Member
MHB
I am posting some AP calculus practice questions on MeWe so thot I would pass them thru here first
The solution is mine...
any typos or suggestions...

$\textbf{Find the Limit of}$
$\displaystyle\lim_{x\to \pi} \dfrac{\cos{x}+\sin{x}+1}{x^2-\pi^2}$
(A) $-\dfrac{1}{2\pi}$
(B) $\dfrac{1}{\pi}$
(C) $1$
(D) DNE
$\textbf{Solution}$
By observation we have $\frac{0}{0}$ so apply L'Hopital's Rule
apply LH'R then plug in $\pi$ and simplify
$$\displaystyle\lim _{x\to \:\pi } \left(\frac{\cos \left(x\right)-\sin \left(x\right)}{2x}\right) =\dfrac{-1-0}{2\pi}=-\dfrac{1}{2\pi} \quad (A)$$

karush said:
I am posting some AP calculus practice questions on MeWe so thot I would pass them thru here first
The solution is mine...
any typos or suggestions...

$\textbf{Find the Limit of}$
$\displaystyle\lim_{x\to \pi} \dfrac{\cos{x}+\sin{x}+1}{x^2-\pi^2}$
(A) $-\dfrac{1}{2\pi}$
(B) $\dfrac{1}{\pi}$
(C) $1$
(D) DNE
$\textbf{Solution}$
By observation we have $\frac{0}{0}$ so apply L'Hopital's Rule
apply LH'R then plug in $\pi$ and simplify
$$\displaystyle\lim _{x\to \:\pi } \left(\frac{\cos \left(x\right)-\sin \left(x\right)}{2x}\right) =\dfrac{-1-0}{2\pi}=-\dfrac{1}{2\pi} \quad (A)$$
Looks good to me.

-Dan

1. What is the purpose of practicing AP calculus questions on limits?

The purpose of practicing AP calculus questions on limits is to improve your understanding and mastery of the concept of limits, which is a fundamental concept in calculus. Practicing these questions can also help you prepare for the AP calculus exam.

2. What is a limit in calculus?

A limit in calculus is a mathematical concept that describes the behavior of a function as the input approaches a certain value. It represents the value that a function approaches as its input gets closer and closer to a specific value.

3. How do I solve a limit in calculus?

To solve a limit in calculus, you need to use algebraic manipulation, substitution, and other mathematical techniques to simplify the expression and evaluate the limit. You may also need to use the properties of limits and apply specific limit rules, such as the product rule or quotient rule.

4. Why is understanding limits important in calculus?

Understanding limits is important in calculus because it is the foundation of many other concepts, such as derivatives and integrals. It helps us understand the behavior of functions and their rates of change, which are essential in many real-world applications.

5. How can I improve my skills in solving limits?

To improve your skills in solving limits, you can practice solving a variety of limit problems, including those involving algebraic functions, trigonometric functions, and exponential functions. You can also review limit rules and properties, and seek help from a teacher or tutor if needed.

Replies
2
Views
1K
Replies
6
Views
1K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
3
Views
889
Replies
2
Views
1K
Replies
4
Views
2K
Replies
3
Views
1K
Replies
1
Views
919
Replies
4
Views
1K