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