• nokia8650
In summary, as t tends to infinity, the function y approaches a limit of 5k + 2. This can be shown by observing that e^(-0.2t) approaches 0 as t increases, causing the entire expression to approach 5k + 2 as t tends to infinity.

#### nokia8650

eg. y = 5ke^(-0.2t) - 5k + 2

How would one show the working to show what happens as t tends to infinity? Would something like this be ok?

as t--> infinity

e^(-0.2t) --> 0

therefore 5ke^(-0.2t) ---> 0

therefore 5ke^(-0.2t) - 5k + 2 --> 5k + 2

therefore y ---> 5k + 2

Thanks

Looks ok. But you left out a minus sign.

nokia8650 said:
How would one show the working …

Hi nokia8650!

I guess it means a delta-epsilon proof.

No, I would not say that "show the working" means a "delta- epsilon" proof. What You have done is correct. You might add something like "Since f(x)= ex increases without bound as x increases, e^(-0.2t) --> 0 as t --> infinity".

## 1. What are limits in mathematics?

Limits are a fundamental concept in mathematics that represents the value that a function approaches as the input approaches a specific value or approaches infinity.

## 2. Why is it important to show your working when dealing with limits?

Showing your working when dealing with limits is important because it allows for a better understanding of the thought process and reasoning behind the solution. It also helps to identify any mistakes made in the calculation.

## 3. How do you find the limit of a function?

The limit of a function can be found by evaluating the function as the input approaches the specific value or infinity. This can be done by using algebraic manipulation, graphing, or using the properties of limits.

## 4. What are the types of limits?

The types of limits include one-sided limits, where the input approaches the specific value from either the left or right side, and two-sided limits, where the input approaches the specific value from both sides. Infinite limits and limits at infinity are also types of limits.

## 5. Can limits be used to solve real-world problems?

Yes, limits can be used to solve real-world problems in various fields such as physics, engineering, and economics. They can be used to model and predict the behavior of systems and help in making informed decisions.