1. lim 4^n+2^n/4^n+1 +2^n-1 2. lim 3^n+1 +4^n-2/4^n+4 +5^n+1

2 câu trả lời

Đáp án:

1) lim =\dfrac{1}{4}

2) \lim \dfrac{3^n+1\:+4^n-2}{4^n+4\:+5^n+1} =0

Giải thích các bước giải:

1) \lim \dfrac{4^n+2^n}{4^{n+1}\:+2^{n-1}}

=\lim \:\dfrac{\dfrac{1}{4}+\dfrac{2^n}{4^{n+1}}}{1+\dfrac{2^{n-1}}{4^{n+1}}}

=\dfrac{\lim \dfrac{1}{4}+\dfrac{2^n}{4^{n+1}}}{\lim \:1+\dfrac{2^{n-1}}{4^{n+1}}}

=\dfrac{\dfrac{1}{4}}{1}

=\dfrac{1}{4}

2) \lim \dfrac{3^n+1\:+4^n-2}{4^n+4\:+5^n+1}

=\lim \:\dfrac{\left(\dfrac{3}{5}\right)^n+\dfrac{1}{5^n}+\left(\dfrac{4}{5}\right)^n-\dfrac{2}{5^n}}{\left(\dfrac{4}{5}\right)^n+\dfrac{4}{5^n}+1+\dfrac{1}{5^n}}

=\dfrac{\lim \left(\dfrac{3}{5}\right)^n+\dfrac{1}{5^n}+\left(\dfrac{4}{5}\right)^n-\dfrac{2}{5^n}}{\lim \left(\dfrac{4}{5}\right)^n+\dfrac{4}{5^n}+1+\dfrac{1}{5^n}}

=\dfrac{0}{1}

=0

Đáp án:

1) \dfrac{1}{4}\\ 2) 0.

Giải thích các bước giải:

1) \lim \dfrac{4^n+2^n}{4^{n+1}+2^{n-1}}\\ =\lim \dfrac{4^n+2^n}{4.4^n+2^{-1}.2^n}\\ =\lim \dfrac{4^n+2^n}{4.4^n+\dfrac{1}{2}.2^n}\\ =\lim \dfrac{1+\left(\dfrac{1}{2}\right)^n}{4+\dfrac{1}{2}.\left(\dfrac{1}{2}\right)^n}\\ =\dfrac{1}{4}\\ 2) \lim \dfrac{3^{n+1}+4^{n-2}}{4^{n+4}+5^{n+1}}\\ =\lim \dfrac{3.3^n+\dfrac{1}{16}.4^n}{4^4.4^n+5.5^n}\\ =\lim \dfrac{3.\left(\dfrac{3}{5}\right)^n+\dfrac{1}{16}.\left(\dfrac{4}{5}\right)^n}{4^4.\left(\dfrac{4}{5}\right)^n+5}\\ =\dfrac{0}{5}\\ =0.

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