tính lim x tiến tới 4 của (2^2018-x^1009)/4-x 05/11/2021 Bởi Quinn tính lim x tiến tới 4 của (2^2018-x^1009)/4-x
Đáp án: $1009.4^{1008}$ Giải thích các bước giải: $\lim_{x\to4}\dfrac{2^{2018}-x^{1009}}{4-x}$ $=\lim_{x\to4}\dfrac{(2^2)^{1009}-x^{1009}}{4-x}$ $=\lim_{x\to4}\dfrac{4^{1009}-x^{1009}}{4-x}$ $=\lim_{x\to4}\dfrac{(4-x)(4^{1008}+x.4^{1007}+x^2.4^{1006}+…+x^{1008})}{4-x}$ $=\lim_{x\to4}4^{1008}+x.4^{1007}+x^2.4^{1006}+…+x^{1008}$ $=4^{1008}+4.4^{1007}+4^2.4^{1006}+…+4^{1008}$ $=1009.4^{1008}$ Bình luận
Ta có $2^{2018}-4^{1009}=2^{2018}-2^{2^{1009}}= 2^{2018}-2^{2018}=0$ $\lim\limits_{x\to 4}\dfrac{2^{2018}-x^{1009}}{4-x}$ $\lim\limits_{x\to 4}\dfrac{(2^{2018}-x^{1009})’}{(4-x)’}$ $=\lim\limits_{x\to 4}\dfrac{-1009x^{1008}}{-1}$ $=1009.4^{1008}$ Bình luận
Đáp án: $1009.4^{1008}$
Giải thích các bước giải:
$\lim_{x\to4}\dfrac{2^{2018}-x^{1009}}{4-x}$
$=\lim_{x\to4}\dfrac{(2^2)^{1009}-x^{1009}}{4-x}$
$=\lim_{x\to4}\dfrac{4^{1009}-x^{1009}}{4-x}$
$=\lim_{x\to4}\dfrac{(4-x)(4^{1008}+x.4^{1007}+x^2.4^{1006}+…+x^{1008})}{4-x}$
$=\lim_{x\to4}4^{1008}+x.4^{1007}+x^2.4^{1006}+…+x^{1008}$
$=4^{1008}+4.4^{1007}+4^2.4^{1006}+…+4^{1008}$
$=1009.4^{1008}$
Ta có $2^{2018}-4^{1009}=2^{2018}-2^{2^{1009}}= 2^{2018}-2^{2018}=0$
$\lim\limits_{x\to 4}\dfrac{2^{2018}-x^{1009}}{4-x}$
$\lim\limits_{x\to 4}\dfrac{(2^{2018}-x^{1009})’}{(4-x)’}$
$=\lim\limits_{x\to 4}\dfrac{-1009x^{1008}}{-1}$
$=1009.4^{1008}$