αំαួα
- αេαាα$y=f(x)=\frac{x^3+4x-5}{x+1}=x^2-x+5-\frac{10}{x+1}$
αំα ាα់
- α ូααααាαីαីααាαα្αោα៖
- $\lim_{x\to\infty}(1+\frac1x)^{3x}$
- $lim_{x\to\infty}(1+\frac{1}{x^2})^{3x-4}$
- $lim_{x\to\infty}(\frac{7x+10}{1+7x})^{\frac x3}$
- $\lim_{x\to 0}x^{x}$
- $\lim_{x\to 1}\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}$
- $\lim_{x\to a}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}$
- $\lim_{x\to 1}\frac{x^2-x\sin x}{x-\sin^2x}$
- $\lim_{x\to +\infty}\left(\frac{x+1}{ln x}\right)$
- $\lim_{x\to +\infty}\frac{lnx+2x^2-2x+1}{x}$
- $\lim_{x\to 0^+}ln(\cos x)lnx$
- $\lim_{x\to +\infty}\frac{e^xlnx+1}{x^2}$
- $\lim_{x\to 0}\frac{\sin x+e^x-1}{x^2+x}$
αំα ាα់
- αោαα្αើ Leinitz's rule α ូααααេαីαី n-th αៃα’αុααα៏αាαα្αោα៖
- $y=x.e^x$
- $y=\frac{1+x}{\sqrt{x}}$
- $y=x^2.e^{-2x}$
- $y=(1-x^3)\cos x$
- $y=x^3.\ln x$
αំα ាα់
α
ូααααាαេαីαេαីn-th
- $y=x^3\sin x$
- $y=\sin x$
- $y=\cos x$
- $y=\frac{1}{x-2}$
- $y=\sqrt{x}$
- $y=\cos 2x$
- $y=\frac{1+x}{1-x}$
- $y=\sin^2x$
- $y=e^{-3x}$
- $y=\ln(x+1)$ by chanchav
αំα ាα់ααិααិα្αា
ααីαាααីαេα’៊ែ
- ααីαាααីαេα’៊ែααំαាα់αួααាααាα៖$a(x)y'+b(x)y=f(x)$αើα្αីαោះα្αាαααីαាααីαេα’៊ែααំαាα់αួααេα្αូαα្αើαីαីα្αាα
α្αោះαាαα្αាα’ាំαេα្αាα - αេα្αូααααេαααីαាααេះα²្ααៅαាαាα$y'+p(x)y=g(x)$αែα$p(x)=\frac{b(x)}{a(x)}$αិα$g(x)=\frac{f(x)}{a(x)}$។ αុαααីαាααោααα្αាα’ាំααេα្αាααឺ$e^{\int p(x)dx}$αេαាα $e^{\int p(x)dx}y'+e^{\int p(x)dx}p(x)y=g(x)e^{\int p(x)dx}\iff (ye^{\int p(x)dx})'=g(x)e^{\int p(x)dx}$
- $\int (ye^{\int p(x)dx})'dx=\int g(x)e^{\int p(x)dx}dx+c\iff y= e^{-\int p(x)}\int g(x)e^{\int p(x)dx}+ e^{-\int p(x)dx}c$
αំα ាα់
I.αេα²្αα’αុααα៏ $f(x)=\sqrt{x+2}$។
1.αα្α ាααាα ំαោះ $x\in[-1,2]$ αេαាα
$\frac14 x+\frac54\le\sqrt{x+2}\le \frac12 x+\frac32$
2.ααα្αាααα្ααααាααើαាαα្αាαិα ។
1.αα្α ាααាα ំαោះ $x\in[-1,2]$ αេαាα
$\frac14 x+\frac54\le\sqrt{x+2}\le \frac12 x+\frac32$
2.ααα្αាααα្ααααាααើαាαα្αាαិα ។
