Calculus question?? Continuity?

Question

f(x)= (sqrt(x))-2/x-4           , x<4

         p                              , x=4

         x²/q                          , x>4

 

 

Find the values of p and q so that f is continuous everywhere

I figured out that p = 1/4 but i can't seem to figure out q

Answer 1

1. simplify the first piece by factoring the denominator (√x - 2)(√x + 2); first factor cancels numerator.

then you can evaluate f(2) using that simplification to see that the left limit at 4 equals 1/4.

Therefore p=1/4 for assure continuity at 4, from the left.

 

2. equate p = 1/4 to the limit of x²/q when x→4⁺

we get 1/4 = 16/q  so q must be 64.

 

CHECK MY WORK so that you can catch any possible error; if it's OK and you check the work, you will understand problems of this kind in the future.