作业帮高数【函数极限】lim (1+1/x)=?x→∞lim(1-3x)∧1/(2x)=?x→0lim[(2x+3)/(2x+1)]∧(x+1)x→∞
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![高数【函数极限】lim (1+1/x)=?x→∞lim(1-3x)∧1/(2x)=?x→0lim[(2x+3)/(2x+1)]∧(x+1)x→∞](/uploads/image/z/4056521-41-1.jpg?t=%E9%AB%98%E6%95%B0%E3%80%90%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E3%80%91lim+%281%2B1%2Fx%29%3D%3Fx%E2%86%92%E2%88%9Elim%281-3x%29%E2%88%A71%2F%282x%29%3D%3Fx%E2%86%920lim%5B%282x%2B3%29%2F%282x%2B1%29%5D%E2%88%A7%28x%2B1%29x%E2%86%92%E2%88%9E)
高数【函数极限】lim (1+1/x)=?x→∞lim(1-3x)∧1/(2x)=?x→0lim[(2x+3)/(2x+1)]∧(x+1)x→∞
高数【函数极限】
lim (1+1/x)=?
x→∞
lim(1-3x)∧1/(2x)=?
x→0
lim[(2x+3)/(2x+1)]∧(x+1)
x→∞
高数【函数极限】lim (1+1/x)=?x→∞lim(1-3x)∧1/(2x)=?x→0lim[(2x+3)/(2x+1)]∧(x+1)x→∞
1.lim (1+1/x)=1+0=1
x→∞
2.lim(1-3x)∧1/(2x)
x→0
=lim(1-3x)^[(-1/3x)*(-3/2)]
x→0
=lim[(1-3x)^(-1/3x)]^(-3/2)
x→0
=e^(-3/2)
3.lim[(2x+3)/(2x+1)]∧(x+1)
x→∞
=lim[1+1/(x+1/2)]^[(x+1/2)+1/2]
x→∞
=lim[1+1/(x+1/2)]^(x+1/2)*[1+1/(x+1/2)]^(1/2)
x→∞
=e*(1+0)^(1/2)
=e