Question

Find k so that the following function is continuous: f(x)={kx8x2if0≤x<5if5≤x.

Answer 1

Check the one-sided limits:

$\displaystyle \lim_{x\to5^-}f(x) = \lim_{x\to5}kx = 5k$

$\displaystyle \lim_{x\to5^+}f(x) = \lim_{x\to5}8x^2 = 200$

If f(x) is to be continuous at x = 5, then these two limits should have the same value, which means

5k = 200

k = 200/5

k = 40