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

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

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limit as x approaches-3/2+of-2/(2x+3)

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

- \infty

Solution steps

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

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

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

For

x

approaching

- \frac{3}{2}

from the right

, x > - \frac{3}{2} \Rightarrow 2 x + 3 > 0

The denominator is a positive quantity approaching 0 from the right

= - 2 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

x \to \infty lim (x^{3} - 7)

x \to 0 lim (4 x + 3 + \frac{1}{x ^{2}})

x \to 0 lim (x (ln (x^{2})))

x \to 0 lim (sin (x) \cdot cos (x))

x \to \frac{π}{2} lim (1 - sin (x))

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