请问这个极限怎么算 要详细步骤 谢谢
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lim(k->无穷) { [k+2+2^(k+1)]/[(k+1)^2 + 3^(k+1)] } .(x-1)^(k+1)
/ { [(k+2^k)/(k^2 + 3^k)] .(x-1)^k }
利用 (x-1)^(k+1)、(x-1)^k = (x-1)
=lim(k->无穷) { [k+2+2^(k+1)]/[(k+1)^2 + 3^(k+1)] } .(x-1)/ [(k+2^k)/(k^2 + 3^k)]
整理算式
=lim(k->无穷) [k+2+2^(k+1)].(k^2 + 3^k).(x-1)/ { (k+2^k). [(k+1)^2 + 3^(k+1)] }
分子分母同时除 (2^k. 3^k)
=lim(k->无穷) [(k+2)/2^k+2].(k^2/3^k + 1).(x-1)
/ { (k/2^k +1). [(k+1)^2/3^k + 3] }
=2.(1)(x-1)/3
=(2/3)(x-1)
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lim(k->无穷) { [k+2+2^(k+1)]/[(k+1)^2 + 3^(k+1)] } .(x-1)^(k+1)
/ { [(k+2^k)/(k^2 + 3^k)] .(x-1)^k }
利用 (x-1)^(k+1)、(x-1)^k = (x-1)
=lim(k->无穷) { [k+2+2^(k+1)]/[(k+1)^2 + 3^(k+1)] } .(x-1)/ [(k+2^k)/(k^2 + 3^k)]
整理算式
=lim(k->无穷) [k+2+2^(k+1)].(k^2 + 3^k).(x-1)/ { (k+2^k). [(k+1)^2 + 3^(k+1)] }
分子分母同时除 (2^k. 3^k)
=lim(k->无穷) [(k+2)/2^k+2].(k^2/3^k + 1).(x-1)
/ { (k/2^k +1). [(k+1)^2/3^k + 3] }
=2.(1)(x-1)/3
=(2/3)(x-1)
/ { [(k+2^k)/(k^2 + 3^k)] .(x-1)^k }
利用 (x-1)^(k+1)、(x-1)^k = (x-1)
=lim(k->无穷) { [k+2+2^(k+1)]/[(k+1)^2 + 3^(k+1)] } .(x-1)/ [(k+2^k)/(k^2 + 3^k)]
整理算式
=lim(k->无穷) [k+2+2^(k+1)].(k^2 + 3^k).(x-1)/ { (k+2^k). [(k+1)^2 + 3^(k+1)] }
分子分母同时除 (2^k. 3^k)
=lim(k->无穷) [(k+2)/2^k+2].(k^2/3^k + 1).(x-1)
/ { (k/2^k +1). [(k+1)^2/3^k + 3] }
=2.(1)(x-1)/3
=(2/3)(x-1)
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