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

The limit as t approaches 4 of (t-sqrt(3t+4))/(4-t) is -5/8

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

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

- \frac{5}{8}

Decimal

- 0.625

Solution steps

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

Rationalize numerator

\frac{t - 3 t + 4}{4 - t} : - \frac{t + 1}{t + 3 t + 4}

= t \to 4 lim (- \frac{t + 1}{t + 3 t + 4})

Plug in the value

t = 4

= - \frac{4 + 1}{4 + 3 \cdot 4 + 4}

Simplify

- \frac{4 + 1}{4 + 3 \cdot 4 + 4} : - \frac{5}{8}

= - \frac{5}{8}

x \to 0 lim (cos (x))

x \to 1 - lim (\frac{5}{x - 1})

x \to 0 lim (13)

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

x \to 3 lim (x^{2} - 8 x + 16)

What is the limit as t approaches 4 of (t-sqrt(3t+4))/(4-t) ?
The limit as t approaches 4 of (t-sqrt(3t+4))/(4-t) is -5/8