a) Ta có (x - 2)2 = 0 và (x - 2)2 > 0 với ∀x ≠ 2 và
(3x - 5) = 3.2 - 5 = 1 > 0.
Do đó
= +∞.
b) Ta có (x - 1) và x - 1 < 0 với ∀x < 1 và
(2x - 7) = 2.1 - 7 = -5 <0.
Do đó
= +∞.
c) Ta có (x - 1) = 0 và x - 1 > 0 với ∀x > 1 và
(2x - 7) = 2.1 - 7 = -5 < 0.
Do đó
= -∞.
Tìm các giới hạn sau:
a) \(\lim\limits_{x\rightarrow2}\dfrac{x-\sqrt{x+2}}{\sqrt{4x+1}-3}\)
b) \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{2x+7}+x-4}{x^3-4x^2+3}\)
\(\lim\limits_{x\rightarrow0}\dfrac{\left(1+3x\right)^3-\left(1-4x\right)^4}{x}\)
\(\lim\limits_{x\rightarrow2}\dfrac{2x^2-5x+2}{x^3-3x-2}\)
\(\lim\limits_{x\rightarrow1}\dfrac{x^4-3x+2}{x^3+2x-3}\)
Tính các giới hạn sau:
a) \(\lim\limits_{x\rightarrow1^+}\dfrac{x^3+x+1}{x-1}\)
b) \(\lim\limits_{x\rightarrow-1^+}\dfrac{3x+2}{x+1}\)
c) \(\lim\limits_{x\rightarrow2^-}\dfrac{x-15}{x-2}\)
Tìm các giới hạn sau:
a) \(\lim\limits_{h\rightarrow0}\dfrac{2\left(x+h\right)^3-2x^3}{h}\)
b) \(\lim\limits_{x\rightarrow1}\dfrac{\left(x+x^2+...+x^{2021}\right)-2021}{x-1}\)
Cho \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-2x+1}{x-1}=3\)
Tính \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{3f\left(x\right)+1}-x-1}{\sqrt{4x+5}-3x-2}\)
Tính các giới hạn sau:
1. \(\lim\limits_{x\rightarrow a}\dfrac{x^2-\left(a+1\right)x+a}{x^3-a^3}\)
2. \(\lim\limits_{x\rightarrow1}\left(\dfrac{1}{1-x}-\dfrac{3}{1-x^3}\right)\)
3. \(\lim\limits_{h\rightarrow0}\dfrac{\left(x+h\right)^3-x^3}{h}\)
\(\lim\limits_{x\rightarrow1}\dfrac{x^3-3x^2+2}{x^2-4x+3}\)
\(\lim\limits_{x\rightarrow1^-}\dfrac{x^2+3x+2}{\left|x+1\right|}\)
\(\lim\limits_{x\rightarrow3}\dfrac{\sqrt[3]{x+5}-2}{x^2-4x+3}\)
Tính các giới hạn sau :
a) \(\lim\limits_{x\rightarrow-3}\dfrac{x+3}{x^2+2x-3}\)
b) \(\lim\limits_{x\rightarrow0}\dfrac{\left(1+x\right)^3-1}{x}\)
c) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-1}{x^2-1}\)
d) \(\lim\limits_{x\rightarrow5}\dfrac{x-5}{\sqrt{x}-\sqrt{5}}\)
e) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-5}{\sqrt{x}+\sqrt{5}}\)
f) \(\lim\limits_{x\rightarrow-2}\dfrac{\sqrt{x^2+5}-3}{x+2}\)
g) \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{x}-1}{\sqrt{x+3}-2}\)
h) \(\lim\limits_{x\rightarrow+\infty}\dfrac{1-2x+3x^3}{x^3-9}\)
i) \(\lim\limits_{x\rightarrow0}\dfrac{1}{x^2}\left(\dfrac{1}{x^2+1}-1\right)\)
j) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\left(x^2-1\right)\left(1-2x\right)^5}{x^7+x+3}\)
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{4x+1}-\sqrt[3]{2x+1}}{x}\)
\(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{4x+5}-3}{\sqrt[3]{5x+3}-2}\)
\(\lim\limits_{x\rightarrow-1}\dfrac{\sqrt[4]{2x+3}+\sqrt[3]{2+3x}}{\sqrt{x+2}-1}\)
