Help with limits?

- anonymous

Help with limits?

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- anonymous

Lemme write out the equation

- anonymous

|dw:1378413041328:dw|

- anonymous

and you wanna know if the function is continuous ?

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## More answers

- anonymous

hint : x^2-a^2 = (x-a)(x+a)

- anonymous

"In exercises 57-60, find the constant a, or the constants a and b, such that the function is continuous on the entire real line."

- anonymous

ok,
hint : x^2-a^2 = (x-a)(x+a)
helps ?

- anonymous

Sure but I don't know what to do after

- anonymous

you need to find the limit of g(x) when x->a

- anonymous

so see if the limit of (x^2-a^2)/(x-a) as x->a
is equal to g(a) = 8

- anonymous

in order to find the limit of (x^2-a^2)/(x-a) as x->a use my hint.

- anonymous

[continuous means lim g(x) as x->a = g(a) ]

- anonymous

@neonpolarbears are you there ?

- anonymous

sorry i'm trying to work out the problem but it's just not making sense

- anonymous

have you calculated the limit of (x^2-a^2)/(x-a) as x->a ?

- anonymous

what did you get ?

- anonymous

does that get factored and cancelled?

- anonymous

yes x-a will cancel

- anonymous

(x^2-a^2)/(x-a) = (x-a)(x+a)/(x-a) = x+a
what is the limit of x+a as x->a ?

- anonymous

2a? idek.

- anonymous

yes!

- anonymous

so now we have
lim g(x) as x->a = 2a
and we need (for continuity) that this limit will be equal to g(a) which is 8.
so what is a then for g(x) to be continuous ?

- anonymous

i'm so lost..

- anonymous

i have no idea how you got x to be approaching a

- anonymous

ok,
continuous function at a point x=a satisfies the condition:
lim g(x) as x->a = g(a)
understand so far ?

- anonymous

kind of

- anonymous

this is the definition of continuous

- anonymous

tbh, constantly rewriting "the lim of so and so" just confuses me

- anonymous

is there a way to solve it without formally writing everything?

- anonymous

now
lim g(x) as x->a = lim (x^2-a^2)/(x-a) as x->a = and as you said = 2a

- anonymous

|dw:1378414759215:dw|

- anonymous

this is what is mean when i write lim of something as x goes to something

- anonymous

i can understand it, just all the letters get overwhelming :/

- anonymous

im sorry for that :(
i will write it

- anonymous

|dw:1378414858659:dw|

- anonymous

|dw:1378414896595:dw|

- anonymous

|dw:1378414954233:dw|

- anonymous

idk what you mean by 2a=g(a)=8

- anonymous

we found that
limg(x) = 2a
x->a
right ?
so now accroding to the definition for g(x) to be continuous
limg(x) = g(a)
x->a
so we need
2a = g(a)
but g(a) = 8 ( it is given in the question)
so
2a = 8

- anonymous

then just solve for a?

- anonymous

yes

- anonymous

sorry that took a long time - this is frustrating

- anonymous

but 2a=8 is not the important part as you know
I hope you understand the procedure

- anonymous

if you have another question and you want to do it together ill be happy to help

- anonymous

(and im sorry for my english)

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