What is the limit as x approaches 16 of (x^3-2x^2-3x)/(sqrt(x+5)-2) ?

The limit as x approaches 16 of (x^3-2x^2-3x)/(sqrt(x+5)-2) is 208(2+sqrt(21))

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limit as x approaches 16 of (x^3-2x^2-3x)/(sqrt(x+5)-2)

x \to 16 lim (\frac{x ^{3} - 2 x ^{2} - 3 x}{x + 5 - 2})

208 (2 + 21)

Decimal

1369.17574 \dots

Solution steps

x \to 16 lim (\frac{x ^{3} - 2 x ^{2} - 3 x}{x + 5 - 2})

Plug in the value

x = 16

= \frac{1 6 ^{3} - 2 \cdot 1 6 ^{2} - 3 \cdot 16}{16 + 5 - 2}

Simplify

\frac{1 6 ^{3} - 2 \cdot 1 6 ^{2} - 3 \cdot 16}{16 + 5 - 2} : 208 (2 + 21)

= 208 (2 + 21)

x \to 5 lim (\frac{x ^{2} - 5 x}{x - 10})

x \to \frac{x}{2} lim (\frac{( sin ( x ) - 1 )}{cos ( x )})

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

x \to - 1 lim (2 x^{2} - 5 x + 3 x)

x \to π lim (\frac{sin ( x )}{tan ( x )})

What is the limit as x approaches 16 of (x^3-2x^2-3x)/(sqrt(x+5)-2) ?
The limit as x approaches 16 of (x^3-2x^2-3x)/(sqrt(x+5)-2) is 208(2+sqrt(21))