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

Find K So That The Following Function Is Continuous Fxkx8x2if0xlt5if5x class=

Sagot :

LammettHashidn

Check the one-sided limits:

[tex]\displaystyle \lim_{x\to5^-}f(x) = \lim_{x\to5}kx = 5k[/tex]

[tex]\displaystyle \lim_{x\to5^+}f(x) = \lim_{x\to5}8x^2 = 200[/tex]

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

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