# Is Your Solution to the Limit Problem Correct?

• transgalactic
In summary, it is common for students to question if they have solved a limit correctly. The best way to check is by plugging the solution back into the original equation. Other ways to verify the solution include using a graphing calculator or seeking guidance from a teacher or tutor. It is important to solve limits correctly as they play a crucial role in calculus and can affect the accuracy of more complex problems. Some common mistakes when solving limits include incorrect factoring, not simplifying the problem, and not considering the direction of the limit. It is important to carefully follow the steps for solving limits to avoid these mistakes.
transgalactic
$$lim_{x->\infty}\frac{3x-cosx}{4x+sinx}=lim_{x->\infty}\frac{\frac{3x-cosx}{x}}{\frac{4x+sinx}{x}}=lim_{x->\infty}\frac{3-0}{4-0}=0.75$$

i thought bounded/infinity=0

??

You have the correct limit, but you should remove the limit operator from the expression below, since you have already "passed to the limit" in the previous expression:
$$lim_{x->\infty}\frac{3-0}{4-0}=0.75$$

thanks

## 1. Did I solve this limit correctly?

This is a common question that many students have after working through a limit problem. The best way to check your answer is to plug your solution back into the original limit equation and see if it works. If it does, then you most likely solved the limit correctly.

## 2. How can I tell if my limit solution is correct?

There are a few ways to check if your limit solution is correct. One method is to use a graphing calculator to graph the function and see if your limit value matches up with the graph. Another method is to plug your solution back into the original limit equation and see if it works.

## 3. What should I do if I am not sure if I solved a limit correctly?

If you are unsure about your limit solution, it is always a good idea to double check your work. You can also ask a teacher or tutor for help and guidance. Practice makes perfect, so keep working on limit problems to improve your skills.

## 4. Why is it important to solve limits correctly?

Limits are an important concept in calculus and are used to calculate derivatives and integrals. If you do not solve limits correctly, it can lead to incorrect solutions for more complex calculus problems. It is important to have a solid understanding of limits in order to succeed in calculus.

## 5. What are some common mistakes when solving limits?

Some common mistakes when solving limits include not factoring correctly, not simplifying the problem before plugging in values, and not paying attention to the direction of the limit (approaching from the left or right). It is important to carefully follow the steps for solving limits to avoid making these mistakes.

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