anonymous
  • anonymous
Help with limits?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Lemme write out the equation
anonymous
  • anonymous
|dw:1378413041328:dw|
anonymous
  • anonymous
and you wanna know if the function is continuous ?

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anonymous
  • anonymous
hint : x^2-a^2 = (x-a)(x+a)
anonymous
  • 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
  • anonymous
ok, hint : x^2-a^2 = (x-a)(x+a) helps ?
anonymous
  • anonymous
Sure but I don't know what to do after
anonymous
  • anonymous
you need to find the limit of g(x) when x->a
anonymous
  • anonymous
so see if the limit of (x^2-a^2)/(x-a) as x->a is equal to g(a) = 8
anonymous
  • anonymous
in order to find the limit of (x^2-a^2)/(x-a) as x->a use my hint.
anonymous
  • anonymous
[continuous means lim g(x) as x->a = g(a) ]
anonymous
  • anonymous
@neonpolarbears are you there ?
anonymous
  • anonymous
sorry i'm trying to work out the problem but it's just not making sense
anonymous
  • anonymous
have you calculated the limit of (x^2-a^2)/(x-a) as x->a ?
anonymous
  • anonymous
what did you get ?
anonymous
  • anonymous
does that get factored and cancelled?
anonymous
  • anonymous
yes x-a will cancel
anonymous
  • 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
  • anonymous
2a? idek.
anonymous
  • anonymous
yes!
anonymous
  • 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
  • anonymous
i'm so lost..
anonymous
  • anonymous
i have no idea how you got x to be approaching a
anonymous
  • anonymous
ok, continuous function at a point x=a satisfies the condition: lim g(x) as x->a = g(a) understand so far ?
anonymous
  • anonymous
kind of
anonymous
  • anonymous
this is the definition of continuous
anonymous
  • anonymous
tbh, constantly rewriting "the lim of so and so" just confuses me
anonymous
  • anonymous
is there a way to solve it without formally writing everything?
anonymous
  • anonymous
now lim g(x) as x->a = lim (x^2-a^2)/(x-a) as x->a = and as you said = 2a
anonymous
  • anonymous
|dw:1378414759215:dw|
anonymous
  • anonymous
this is what is mean when i write lim of something as x goes to something
anonymous
  • anonymous
i can understand it, just all the letters get overwhelming :/
anonymous
  • anonymous
im sorry for that :( i will write it
anonymous
  • anonymous
|dw:1378414858659:dw|
anonymous
  • anonymous
|dw:1378414896595:dw|
anonymous
  • anonymous
|dw:1378414954233:dw|
anonymous
  • anonymous
idk what you mean by 2a=g(a)=8
anonymous
  • 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
  • anonymous
then just solve for a?
anonymous
  • anonymous
yes
anonymous
  • anonymous
sorry that took a long time - this is frustrating
anonymous
  • anonymous
but 2a=8 is not the important part as you know I hope you understand the procedure
anonymous
  • anonymous
if you have another question and you want to do it together ill be happy to help
anonymous
  • anonymous
(and im sorry for my english)

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