Question

if fx = {x^2+k when x>0 and if fx is continous at x=0 then k =
-x^2-k when x<0

Answer 1

Answer:

Value of k = 0

Step-by-step explanation:

Since the question isn't typed properly, I'm not sure what exactly you need,but I assume this is your question :

If f (x) = x² + k,x > 0 and f(x) = -x² - k,x <0 and f(x) is continuous at 0, find the value of k.

So,we know that if a function is continuous at any point,the left hand limit (LHL) and the right hand limit (RHL) at that concerned point is equal i.e RHL = LHL.

So, here we will check the limit of the function at 0.

Now let's proceed with the solution.

LHL (lim x → 0-) :

=> lim x → 0- [-x² - k]

Substitute the limiting value,

=> -0² - k

=> 0 - k

=> -k

So,the LHL = -k

Now, let's check the RHL (lim x → 0+) :

=> lim x → 0 [x² + k]

Substitute the limiting value,

=> 0² + k

=> 0 + k

=> k

So,RHL = k

Now, equate RHL and LHL,

k = -k

k + k = 0

2k = 0

k = 0/2

k = 0