What is the limit as x approaches 4 of (4-sqrt(4+3x))/(4-x) ?

The limit as x approaches 4 of (4-sqrt(4+3x))/(4-x) is 3/8

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limit as x approaches 4 of (4-sqrt(4+3x))/(4-x)

x \to 4 lim (\frac{4 - 4 + 3 x}{4 - x})

\frac{3}{8}

Decimal Notation

0.375

Solution steps

x \to 4 lim (\frac{4 - 4 + 3 x}{4 - x})

Multiply by the conjugate of

4 - 4 + 3 x : \frac{- 3 x + 12}{4 + 4 + 3 x}

= x \to 4 lim (\frac{\frac{- 3 x + 12}{4 + 4 + 3 x}}{4 - x})

Simplify

\frac{\frac{- 3 x + 12}{4 + 4 + 3 x}}{4 - x} : \frac{3}{4 + 3 x + 4}

= x \to 4 lim (\frac{3}{4 + 3 x + 4})

Plug in the value

x = 4

= \frac{3}{4 + 3 \cdot 4 + 4}

Simplify

\frac{3}{4 + 3 \cdot 4 + 4} : \frac{3}{8}

= \frac{3}{8}

x \to - 1 + lim (2^{\frac{1}{x + 1}})

x \to 25 lim (5 - x)

x \to 2 lim (\frac{x - 3}{x + 2})

x \to \frac{1}{8} lim (\frac{1}{x} + x - 1)

x \to 0 lim (\frac{( 2 + x )}{1 + x})

What is the limit as x approaches 4 of (4-sqrt(4+3x))/(4-x) ?
The limit as x approaches 4 of (4-sqrt(4+3x))/(4-x) is 3/8