Question

Use the given graph to find delta (precise limit definition, section).

Answer 1

if \[0 < \left| x-a \right| < \delta \] then \[\left| f(x) - L \right| < \]
So, the left "?" corresponds to the y-value of 0.5. Set \[0.5 = x^2\] to get 0.25 for x. Use the limit of 1 for 1-0.25 = 0.75. Hence, \[\delta \le 0.75\]

Answer 2

\[\left| f(x)-L \right| < \epsilon\]

Answer 3

HI!!

Answer 4

Hello

Answer 5

this might be easier to do with \(\epsilon,\delta\) but it gave you a number to work with

Answer 6

yea, is the answer 0.75?

Answer 7

This is an even number, hence I can't check for a solution :(

Answer 8

\[|x^2-1|<\frac{1}{2}\\
-\frac{1}{2}<x^2-1<\frac{1}{2}\\
\frac{1}{2}<x^2<\frac{3}{2}\] so \[\sqrt{\frac{1}{2}}<x<\sqrt{\frac{3}{2}}\]

Answer 9

so we would use the square root of (1/2) and subtract it from the limit of 1 to find the delta?

Answer 10

now subtract 1 all the way across

Answer 11

and take the absolute value of the bigger one

Answer 12

@misty1212 would the answer be 0.22 for delta?

Answer 13

\[1-\sqrt{1/2} = 0.29\]
\[1-\sqrt{3/2}= -0.22\] --> \[\left| -0.22 \right| = 0.22\].
So, the delta is 0.22?

Answer 14

i think you might have made an error

Answer 15

\[\sqrt{\frac{1}{2}}<x<\sqrt{\frac{3}{2}}\] now you want to subtract 1 all the way across, not add

Answer 16

\[\sqrt{\frac{1}{2}}<x<\sqrt{\frac{3}{2}}\\\sqrt{\frac{1}{2}}-1<x-1<\sqrt{\frac{3}{2}}-1\]

Answer 17

How come we are doing \[\sqrt{\frac{ 1 }{ 2 }}-1\] instead of \[1-\sqrt{\frac{ 1 }{ 2 }}\]?

Answer 18

Because if \(a<x<b\), then \(a-1<x-1<b-1\).

Answer 19

\[\delta \le 0.29\] would be the answer?