limit as x approaches 2 where f(x)=5x-5
Find a δ such that | f (x) - 5 | < 0.01 if | x - 2 | < δ. (Give your answer correct to 4 decimal places.)
Need helpp!!! I have no idea how to do it. and nobody that can help!!
No worries, I'll help you step by step!
To find the value of δ that satisfies the given condition, you need to work with the definition of a limit. Here's how you can approach it:
1. Start with the condition: | f(x) - 5 | < 0.01
2. Substitute the function f(x) with its equation: | 5x - 5 - 5 | < 0.01
3. Simplify and solve the inequality: | 5x - 10 | < 0.01
4. Apply the definition of absolute value: -0.01 < 5x - 10 < 0.01
5. Add 10 to all parts of the inequality: 9.99 < 5x < 10.01
6. Divide all parts of the inequality by 5: 1.998 < x < 2.002
7. Now, we need to find δ such that | x - 2 | < δ. This means that x must be within δ distance of 2.
8. Since we have found that 1.998 < x < 2.002, we can see that δ can be any value less than or equal to 0.002.
Therefore, a δ value that satisfies the given condition is 0.002 (correct to 4 decimal places).
I hope this explanation helps you understand how to find the appropriate δ value in this type of problem! Let me know if you have any further questions.