Solve lim1/x_{n}=1/x

$$\lim \frac { 1 } { x _ { n } } = \frac { 1 } { x }$$

Solve for l

$$l=\frac{1}{Im(\frac{1}{x_{n}})x}$$

$$x_{n}\neq 0\text{ and }x\neq 0\text{ and }Im(\frac{1}{x_{n}})\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$lIm(\frac{1}{x_{n}})x=1$$

The equation is in standard form.

$$Im(\frac{1}{x_{n}})xl=1$$

Divide both sides by Im(x_{n}^{-1})x.

$$\frac{Im(\frac{1}{x_{n}})xl}{Im(\frac{1}{x_{n}})x}=\frac{1}{Im(\frac{1}{x_{n}})x}$$

Dividing by Im(x_{n}^{-1})x undoes the multiplication by Im(x_{n}^{-1})x.

$$l=\frac{1}{Im(\frac{1}{x_{n}})x}$$

Solve for x

$$x=\frac{1}{Im(\frac{1}{x_{n}})l}$$

$$Im(\frac{1}{x_{n}})\neq 0\text{ and }l\neq 0\text{ and }x_{n}\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$lIm(\frac{1}{x_{n}})x=1$$

The equation is in standard form.

$$Im(\frac{1}{x_{n}})lx=1$$

Divide both sides by lIm(x_{n}^{-1}).

$$\frac{Im(\frac{1}{x_{n}})lx}{Im(\frac{1}{x_{n}})l}=\frac{1}{Im(\frac{1}{x_{n}})l}$$

Dividing by lIm(x_{n}^{-1}) undoes the multiplication by lIm(x_{n}^{-1}).

$$x=\frac{1}{Im(\frac{1}{x_{n}})l}$$

Variable x cannot be equal to 0.

$$x=\frac{1}{Im(\frac{1}{x_{n}})l}\text{, }x\neq 0$$