lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.
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![lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.](/uploads/image/z/5222174-14-4.jpg?t=lim%28x%E2%86%92-2%29%28ax%2Bb%29%2F%28x%2B2%29%3D4%2Ca%E3%80%81b%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E6%B1%82a%E3%80%81b.)
lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.
lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.
lim(x→-2)(ax+b)/(x+2)=4,a、b为常数,求a、b.
lim(x→-2)(ax+b)/(x+2)=lim(x→-2)[a(x+2)+b-2a]/(x+2)=a+lim(x→-2)(b-2a)/(x+2)
由于lim(x→-2)1/(x+2)=∞
所以lim(x→-2)(b-2a)/(x+2)为常数的条件是b-2a=0,即b=2a
那么lim(x→-2)(ax+b)/(x+2)=a=4,故b=8
分子在x=-2时为零,故-2a+b=0,且左边的极限为a/1=4,故b=8,a=4
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