Posted by **Tommy feels dumb** on Wednesday, May 7, 2014 at 1:25pm.

consider the statement

lim x-6x+11x-6 / x-1 = 2

x->1

Using the definition of the limit, state what must be true for the above limit to hold, that is, for

every ..., there is ..., so that.... Use a specific function and limit not just f and L.

Verify the limit is true by finding as an expression of ϵ.

Draw a picture illustrating the relation between ϵ, and the function.

i am at hulk422 at g mail . com

- Calculus (lim) -
**Steve**, Wednesday, May 7, 2014 at 5:02pm
x^3-6x^2+11x-6 = (x-1)(x-2)(x-3)

So, for all x≠1,

f(x) = (x-2)(x-3)

as x->1, f(x)->2 since both factors are negative

we need to show that for every ϵ>0 there is a δ such that

f(x+δ)-2 < ϵ

we can dispense with the absolute value stuff, since f(x) > 0 and we are taking the upper limit. So, we just need to show that we can solve for δ, no matter which small ϵ we choose.

((x+δ)-2)((x+δ)-3)-2 < ϵ

That's just a simple quadratic, which will have two real roots.

## Answer this Question

## Related Questions

- Calculus - HELP....last question SOS HELP Consider the statement lim X-->1 X...
- Calculus. Limits. Check my answers, please! :) - 4. lim (tanx)= x->pi/3 -(...
- Calculus - I have two similar problems that I need help completing. Please show ...
- Calculus - Let f be a function defined for all real numbers. Which of the ...
- calculus again - Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily ...
- Calculus - Find the indicated limits. If the limit does not exist, so state, or ...
- Calculus - Find the indicated limits. If the limit does not exist, so state, or ...
- calculus - Find lim (with x under it) (x^2-1)/x or state that the limit does...
- calc - need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting ...
- Calculus - Got a midterm worksheet. Realized how confused I am. Here are some ...

More Related Questions