求极限 1.lim(x趋于正无穷)4x^2-3x+1/2x^2-6x+52.lim(x趋于正无穷) (2x-1/2x+1)^x+13.lim(x→1) sin(x-1)/x-1有详细过程,准确性高的,
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![求极限 1.lim(x趋于正无穷)4x^2-3x+1/2x^2-6x+52.lim(x趋于正无穷) (2x-1/2x+1)^x+13.lim(x→1) sin(x-1)/x-1有详细过程,准确性高的,](/uploads/image/z/813136-40-6.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90+1.lim%28x%E8%B6%8B%E4%BA%8E%E6%AD%A3%E6%97%A0%E7%A9%B7%294x%5E2-3x%2B1%2F2x%5E2-6x%2B52.lim%28x%E8%B6%8B%E4%BA%8E%E6%AD%A3%E6%97%A0%E7%A9%B7%29+%282x-1%2F2x%2B1%29%5Ex%2B13.lim%EF%BC%88x%E2%86%921%EF%BC%89+sin%EF%BC%88x-1%EF%BC%89%2Fx-1%E6%9C%89%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B%2C%E5%87%86%E7%A1%AE%E6%80%A7%E9%AB%98%E7%9A%84%2C)
求极限 1.lim(x趋于正无穷)4x^2-3x+1/2x^2-6x+52.lim(x趋于正无穷) (2x-1/2x+1)^x+13.lim(x→1) sin(x-1)/x-1有详细过程,准确性高的,
求极限 1.lim(x趋于正无穷)4x^2-3x+1/2x^2-6x+5
2.lim(x趋于正无穷) (2x-1/2x+1)^x+1
3.lim(x→1) sin(x-1)/x-1有详细过程,准确性高的,
求极限 1.lim(x趋于正无穷)4x^2-3x+1/2x^2-6x+52.lim(x趋于正无穷) (2x-1/2x+1)^x+13.lim(x→1) sin(x-1)/x-1有详细过程,准确性高的,
1、
x→+∞
lim (4x^2-3x+1) / (2x^2-6x+5)
=lim (4x^2-3x+1)/x^2 / (2x^2-6x+5)/x^2
=lim (4-(3/x)+(1/x^2)) / (2-(6/x)+(5/x^2))
=(4-0+0) / (2-0+0)
=4/2
=2
2、
x→+∞
lim [(2x-1)/(2x+1)]^(x+1)
=lim [(2x+1-2)/(2x+1)]^(x+1)
=lim [1-2/(2x+1)]^(x+1)
=lim [1-2/(2x+1)]^[2(x+1)/2]
=lim [1-2/(2x+1)]^[(2x+1+1)/2]
=lim [1-2/(2x+1)]^[(2x+1)/2] * lim [1-2/(2x+1)]^[1/2]
=lim [1-2/(2x+1)]^[(2x+1)/2] * 1
=lim [1-2/(2x+1)]^[(2x+1)/-2 * -1]
=[lim [1-2/(2x+1)]^[(2x+1)/-2]]^(-1)
根据重要的极限:lim(x→∞) (1+1/x)^x=e
=e^(-1)
3、
x→1
lim sin(x-1) / (x-1)
换元:t=x-1
=lim(t→0) sint / t
根据重要的极限:lim sinx/x=1
=1
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1.lim(x趋于正无穷)(4x^2-3x+1)/(2x^2-6x+5)
=lim(x趋于正无穷)(4-3/x+1/x^2)/(2-6/x+5/x^2)
=4/2
=2
2.lim(x趋于正无穷) (2x-1/2x+1)^x+1
=lim(x趋于正无穷) (2x-0+1)^x+1
=lim(x趋于正无穷) (2x+1)^x+1
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1.lim(x趋于正无穷)(4x^2-3x+1)/(2x^2-6x+5)
=lim(x趋于正无穷)(4-3/x+1/x^2)/(2-6/x+5/x^2)
=4/2
=2
2.lim(x趋于正无穷) (2x-1/2x+1)^x+1
=lim(x趋于正无穷) (2x-0+1)^x+1
=lim(x趋于正无穷) (2x+1)^x+1
=+∞
3.lim(x→1) sin(x-1)/(x-1)
=lim(x→1)(x-1)/(x-1)
=1
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