Question

consider limx->2 f(x), where f(x)=4x-1
show that |f(x)-7|<4delta if 0<|x-2| 12 years ago

Answer 1

I'll see what I can do for you. You may have to insert some nuances that I am likely to leave out having not rigorously proved a limit in several years. Ok here goes:\[\left| f(x)-7 \right|=\left| (4x-1)-7 \right|=\left| 4x-8 \right|=4\left| x-2 \right|\]
So\[\left| f(x)-7 \right|=4\left| x-2 \right|<4\delta\]
from this we can tell that\[0<\left| x-2 \right|<\delta\]
as desired.

Answer 2

I guess actually it should be from\[0<\left| x-2 \right|<\delta\] we can see that the limit exists.. lol. Whatever. I'm pretty sure the math is right anyway. This is what happens when you don't take a mathematical reasoning or proofs class.

Answer 3

ok let try to figure out your steps

Answer 4

so I did get that part right in the work I did can you help me with part b

Answer 5

What's the part b?