What is the limit as t approaches 2-of-(3t)/(t-2) ?

The limit as t approaches 2-of-(3t)/(t-2) is infinity

limit as t approaches 2-of-(3t)/(t-2)

t \to 2 - lim (- \frac{3 t}{t - 2})

\infty

Solution steps

t \to 2 - lim (- \frac{3 t}{t - 2})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - 3 \cdot t \to 2 - lim (\frac{t}{t - 2})

Divide by highest denominator power:

\frac{1}{1 - \frac{2}{t}}

= - 3 \cdot t \to 2 - lim (\frac{1}{1 - \frac{2}{t}})

For

t

approaching

2

from the left

, t < 2 \Rightarrow 1 - \frac{2}{t} < 0

The denominator is a negative quantity approaching 0 from the left

= - 3 (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

d er i v a t i v e 11 x^{2} e^{x}

n = 0 \sum \infty \frac{e ^{n}}{( n ! )}

\int (e^{4 x}) d x

\frac{d N}{d t} + N = Nt e^{t + 3}

d er i v a t i v e 5 x + 6

What is the limit as t approaches 2-of-(3t)/(t-2) ?
The limit as t approaches 2-of-(3t)/(t-2) is infinity