Some help needed!

[Artemis01]

let f(x) be a function defined as f(x) = {1/2x-1 , x>1,
............................................................ 4x-3 , ....x<or=1}
i) Evaluate lim_{x --> 1} f(x)


ii) determine whether the function f(x) is continuous at x=1. justify your answer

 

[lex]

[MATH]\frac{1}{2x-1}[/MATH] is continuous on [MATH][1,\infty)[/MATH]so the limit of f (at 1) from the right is [MATH]\frac{1}{2(1)-1}=1[/MATH]
[MATH]4x-3[/MATH] is continuous on [MATH](-\infty,1][/MATH]so the limit of f (at 1) from the left is 4(1)-3=1

The left and right limits of f at 1 exist and are equal, therefore [MATH]\lim_{x \to 1} f(x)[/MATH] exists and equals 1

You should be able to complete the question.

 

[HallsofIvy]

Lex is assuming you meant 1/(2x- 1) but what you wrote was 1/2x- 1= (1/2x)- 1. Which did you mean?

As x goes to 1 from above 1/2x goes to 1/2 so 1/2x- 1 goes to 1/2- 1= -1/2.