Помогите решить пожалуйста, хотя бы несколько

1. [latex] \lim_{n \to \infty} \frac{sin(n^3-4)+2n}{3n^2-1}= \lim_{n \to \infty} \frac{2n}{3n^2} = \lim_{n \to \infty} \frac{2}{3n} =0 [/latex] 2. [latex] \lim_{n \to \infty} \frac{1,5n^2+2n-1}{2n^2+n-8} = \lim_{n \to \infty} \frac{1,5n^2}{2n^2}=\frac{1,5}{2}=0,75[/latex] 3. [latex] \lim_{n \to \infty} \frac{ \sqrt{3n-1}-\sqrt{2n+1} }{\sqrt{n}} =\lim_{n \to \infty} \frac{ \sqrt{3n^2-n}-\sqrt{2n^2+n} }{n}= \\ \lim_{n \to \infty} \frac{ n \sqrt{3} -n \sqrt{2} }{n} = \sqrt{3} - \sqrt{2}[/latex] 4. [latex] \lim_{x \to 1} \frac{sin( \frac{ \pi x}{2} )}{x^2+x-1} = \lim_{x \to 1} \frac{ 1}{1} =1[/latex] 5. [latex] \lim_{x \to -3} \frac{x^2+2x-3}{x^2+x-6} [/latex] x²+2x-3=0 D=2²+4*3=4+12=16    √D=4 x₁=(-2-4)/2=-3 x₂=(-2+4)/2=1 x²+2x-3=(x+3)(x-1) x²+x-6=0 D=1+4*6=25  √D=5 x₁=(-1-5)/2=-3 x₂=(-1+5)/2=2 x²+x-6=(x+3)(x-2) [latex]\lim_{x \to -3} \frac{x^2+2x-3}{x^2+x-6} =\lim_{x \to -3} \frac{(x+3)(x-1)}{(x+3)(x-2)}=\lim_{x \to -3} \frac{x-1}{x-2}= \frac{-4}{-5} =0,8 [/latex] 6. [latex] \lim_{x \to 0} \frac{sin(x^2)}{xtg(2x)}= \lim_{x \to 0} \frac{x^2}{2x^2}= \frac{1}{2} [/latex]

1. [latex] \lim_{n \to \infty} \frac{sin(n^3-4)+2n}{3n^2-1}=\lim_{n \to \infty} \frac{ \frac{sin(n^3-4)}{n^2} + \frac{2}{n} }{3- \frac{1}{n^2} }=0 [/latex] 2. [latex]\lim_{n \to \infty} \frac{1,5n^2+2n-1}{2n^2+n-8}=\lim_{n \to \infty} \frac{1,5+ \frac{2}{n} - \frac{1}{n^2} }{2+ \frac{1}{n} - \frac{8}{n^2} }=0,75[/latex] 3. [latex]\lim_{n \to \infty} \frac{ \sqrt{3n-1}- \sqrt{2n+1}}{\sqrt n}=\lim_{n \to \infty} \frac{3n-1-(2n+1)}{\sqrt{n}(\sqrt{3n-1}+\sqrt{2n+1})}=[/latex][latex]\lim_{n \to \infty} \frac{n-2}{n(\sqrt{3- \frac{1}{n} }+\sqrt{2+\frac{1}{n}})}=\lim_{n \to \infty} \frac{1- \frac{2}{n} }{\sqrt{3- \frac{1}{n} }+\sqrt{2+\frac{1}{n}}}=\frac{1}{\sqrt3+\sqrt2}=\sqrt3-\sqrt2[/latex] 4. [latex]\lim_{x \to1} \frac{sin( \frac{ \pi x}{2})}{x^2+x-1}=\frac{sin \frac{ \pi}{2}}{1^2+1-1}=sin \frac{ \pi}{2}}=1[/latex] 5. [latex]\lim_{x \to-3} \frac{x^2+2x-3}{x^2+x-6}=\lim_{x \to-3} \frac{(x-1)(x+3)}{(x-2)(x+3)}=\lim_{x \to-3} \frac{x-1}{x-2}=\frac{-4}{-5}=\frac{4}{5}[/latex] 6. [latex]\lim_{x \to0} \frac{sin(x^2)}{xtg(2x)}=\lim_{x \to0} \frac{x^2}{x*2x}=\lim_{x \to0} \frac{x^2}{2x^2}=\frac{1}{2}[/latex] 7. [latex]\lim_{x \to \infty}( \frac{x^2+2}{x^2+1})^{x^2+3x-1}=\lim_{x \to \infty}( \frac{(x^2+1)+1}{x^2+1})^{(x^2+1)+(3x-2)}=[/latex][latex]\lim_{x \to \infty}[(1+\frac{1}{x^2+1})^{x^2+1}*(1+\frac{1}{x^2+1})^{3x-2}]=[/latex][latex]\lim_{x \to \infty}(1+\frac{1}{x^2+1})^{x^2+1}*\lim_{x \to \infty}(1+\frac{1}{x^2+1})^{3x-2}=[/latex][latex]e*\lim_{x \to \infty}(1+\frac{1}{x^2+1})^{3x-2}[/latex] 7-й пока не выходит...