Re: [微分] 94政大資管
※ 引述《bitchdog (PEaCE)》之銘言：
: Let f(x)={ √¯¯¯
: (x+4) -3
: ------------ , x≠5
: x-5
: {f(5)=c
: and let f be continuous at x=5 then c=?
√(x+4) - 3
------------- , x≠5
x - 5
f(x) =
f(5) = c
f(x) is continuous => lim f(x) = f(5) = c
x→5
√(x+4) - 3
lim -------------
x→5 x - 5
(√(x+4) - 3)(√(x+4) + 3)
= lim ----------------------------
x→5 (x-5)(√(x+4) + 3)
x + 4 - 9
= lim --------------------
x→5 (x-5)(√(x+4) + 3)
x - 5
= lim --------------------
x→5 (x-5)(√(x+4) + 3)
1
= lim --------------
x→5 √(x+4) + 3
1
= -------------
√(5+4) + 3
1 1 1
= ---------- = ------- = ---
√9 + 3 3 + 3 6
1
所以 c = ---
6
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10/24 20:45, , 1F
10/24 20:45, 1F
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