Задачи для самостоятельного решения

1. $$\lim_{x \to \infty}{\frac{\left(1+x^{11}+7x^{13} \right)^3}{\left(1+x^4 \right)^{10}}}$$

2. $$\lim_{x \to 5}{\frac{\sqrt{x+11}-2\sqrt{x-1}}{x^2-25}}$$

3. $$\lim_{x \to 0}{\frac{\cos{3x}-\cos{7x}}{x^2}}$$

4. $$\lim_{x \to 0}{\frac{\cos 3x^3 -1}{\sin^6{2x}}}$$

5. $$\lim_{x \to \infty}{\left( \frac{x}{2x+1} \right)^{x^2}}$$

6. $$\lim_{x \to 0}{\frac{\ln {\cos 5x}}{\ln \cos 4x}}$$

7. $$\lim_{x \to 0}{ \left( 1+3x^4\right)^{1/\sin^2{x}} }$$

8. $$\lim_{x \to \pi /2}{\left( \sin x\right)^{tg^2{x}}}$$

9. $$\lim_{x \to 0}{\frac{x\sin 2x}{1+\cos (x-3\pi)}}$$

10. $$\lim_{x \to 0}{ \left( \frac{1+x\cdot 3^x}{1+x\cdot 7^x} \right)^{1/tg^{2}x }}$$

11. $$\lim_{x \to \infty}{\left( e^{1/x}+\frac{1}{x}\right)^x}$$

12. $$\lim_{x \to 7}{\frac{\ln (8-x)}{\sin \pi x}}$$

13. $$\lim_{x \to 0}{\frac{\sqrt{\cos x}-\sqrt[3]{\cos x}}{\sin^2 x}}$$