What is the limit as x approaches 7 of (x-7)/(sqrt(x-4)-\sqrt{3)} ?

The limit as x approaches 7 of (x-7)/(sqrt(x-4)-\sqrt{3)} is 2sqrt(3)

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limit as x approaches 7 of (x-7)/(sqrt(x-4)-\sqrt{3)}

x \to 7 lim (\frac{x - 7}{x - 4 - 3})

23

Decimal Notation

3.46410 \dots

Solution steps

x \to 7 lim (\frac{x - 7}{x - 4 - 3})

Rationalize denominator

\frac{x - 7}{x - 4 - 3} : x - 4 + 3

= x \to 7 lim (x - 4 + 3)

Plug in the value

x = 7

= 7 - 4 + 3

Simplify

= 23

\int e^{\frac{- x}{10}} d x

y = 2 x^{3} - x^{2} + 6, (2, 18)

y^{^{'}} = \frac{y}{x} + tan (\frac{y}{x})

4 y^{^{''}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 3

\frac{\partial}{\partial x} (x e^{- a x^{2}})

What is the limit as x approaches 7 of (x-7)/(sqrt(x-4)-\sqrt{3)} ?
The limit as x approaches 7 of (x-7)/(sqrt(x-4)-\sqrt{3)} is 2sqrt(3)