1) [latex]\lim_{x \to \infty} \frac{100}{x} [/latex] 2) [latex]\lim_{x \to \infty} (5-\frac{40}{3x^{2}} ) [/latex] 3) [latex]\lim_{x \to \infty} \frac{4x-10}{3+x} [/latex] 4)[latex]\lim_{x \to \infty} (\frac{5x^{3}-7x}{x^{2}+8...
1) [latex]\lim_{x \to \infty} \frac{100}{x} [/latex] 2) [latex]\lim_{x \to \infty} (5-\frac{40}{3x^{2}} ) [/latex] 3) [latex]\lim_{x \to \infty} \frac{4x-10}{3+x} [/latex] 4)[latex]\lim_{x \to \infty} (\frac{5x^{3}-7x}{x^{2}+8x})[/latex] 5) [latex]\lim_{x \to 1} \frac{x^{2}-1}{x-1}[/latex] 6) [latex]\lim_{x \to 0} \frac{sin 4x}{2x}[/latex] 7)[latex]\lim_{x \to 0} \frac{tg 5x}{sin15x}[/latex] 8) [latex]\lim_{x \to 0} (1+3x)^{\frac{1}{2}} [/latex] 9) [latex]\lim_{x \to \infty} (1-\frac{1}{2x})^{x}[/latex]
Гость
Ответ(ы) на вопрос:
Гость[latex]lim_{x->\infty} \frac{100}{x}=0[/latex]
[latex]lim_{x->\infty} (5-\frac{40}{3x^2})=5-0=5[/latex]
[latex]lim_{x->\infty} \frac{4x-10}{3+x}=lim_{x->\infty} \frac{4-\frac{10}{x}}{\frac{3}{x}+1}=\\\\ \frac{4-0}{0+1}=4[/latex]
[latex]lim_{x->\infty} \frac{5x^3-7x}{x^2+8x}=\\\\lim_{x->\infty} \frac{5x-\frac{7}{x^2}}{1+\frac{8}{x}}=\infty[/latex]
[latex]lim_{x->1} \frac{x^2-1}{x-1}=lim_{x->1} \frac{(x-1)(x+1)}{x-1}=\\\\lim_{x->1} (x+1)=1+1=2[/latex]
[latex]lim_{x->0} \frac{sin (4x)}{2x}=lim_{x->0} (\frac{sin(4x)}{(4x)}*2)=1*2=2[/latex]
[latex]lim_{x->0} \frac{tg(5x)}{sin(15x)}=\\\\lim_{x->0} (\frac{tg(5x)}{5x}*\frac{15x}{sin(15x)}*\frac{1}{3}=\\\\1*1*\frac{1}{3}=\frac{1}{3}[/latex]
[latex]lim_{x->0} (1+3x)^{\frac{1}{2}}=(1+3*0)^{\frac{1}{2}}=1[/latex]
[latex]lim_{x->\infty}(1-\frac{1}{2x})^x=(lim_{x->\infty} (1-\frac{1}{2x})^{-2x})^{-\frac{1}{2}}=\\\\e^{-\frac{1}{2}}=\frac{1}{\sqrt{e}}[/latex]
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