Evaluate ${\lim }_{x\to 6}\frac{\sqrt{x+115}-11}{x-6}$.

Evaluate ${\lim }_{x\to 36}\frac{x-36}{\sqrt{x}-6}$.

Evaluate ${\lim }_{x\to -5}\frac{\sqrt{x+54}-7}{x+5}$.

Evaluate ${\lim }_{x\to 5}\frac{\sqrt{x+95}-10}{x-5}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(5x\right)}{\sin \left(8x\right)}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{1-\cos \left(4x\right)}{9x^2}$, with $x$ in radians.

What is the correct first move for ${\lim }_{x\to 1}\frac{\sqrt{x+15}-4}{x-1}$, and what is the limit?

Evaluate ${\lim }_{x\to 169}\frac{x-169}{\sqrt{x}-13}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(9x\right)}{8x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(4x\right)}{5x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 121}\frac{x-121}{\sqrt{x}-11}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(6x\right)}{5x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(8x\right)}{7x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{\tan \left(8x\right)}{7x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{1-\cos \left(5x\right)}{2x^2}$, with $x$ in radians.

Evaluate ${\lim }_{x\to -1}\frac{\sqrt{x+122}-11}{x+1}$.

Evaluate ${\lim }_{x\to -5}\frac{\sqrt{x+41}-6}{x+5}$.

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{-9+h}-\frac{1}{-9}}{h}$.

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{5+h}-\frac{1}{5}}{h}$.

Evaluate ${\lim }_{x\to 0}\frac{1-\cos \left(7x\right)}{2x^2}$, with $x$ in radians.

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{11+h}-\frac{1}{11}}{h}$.

Evaluate ${\lim }_{x\to 9}\frac{x-9}{\sqrt{x}-3}$.

Evaluate ${\lim }_{x\to 196}\frac{x-196}{\sqrt{x}-14}$.

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{10+h}-\frac{1}{10}}{h}$.

Evaluate ${\lim }_{x\to 0}\frac{1-\cos \left(5x\right)}{2x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(8x\right)}{\sin \left(3x\right)}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(5x\right)}{4x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to -2}\frac{\sqrt{x+38}-6}{x+2}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(2x\right)}{8x}$, with $x$ in radians.

What is the correct first move for ${\lim }_{x\to 4}\frac{\sqrt{x+77}-9}{x-4}$, and what is the limit?

What is the correct first move for ${\lim }_{x\to -2}\frac{\sqrt{x+18}-4}{x+2}$, and what is the limit?

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(5x\right)}{8x}$, with $x$ in radians.

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{-6+h}-\frac{1}{-6}}{h}$.

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{-3+h}-\frac{1}{-3}}{h}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(2x\right)}{7x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to -6}\frac{\sqrt{x+150}-12}{x+6}$.

Evaluate ${\lim }_{x\to -5}\frac{\sqrt{x+105}-10}{x+5}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(4x\right)}{\sin \left(9x\right)}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{1-\cos \left(3x\right)}{6x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{1-\cos \left(2x\right)}{9x}$, with $x$ in radians.