Find the following: \lim_{x\to-2}(\frac{1}{x^2}+\frac{1}{x^3+4}) E

Question

Find the following:

lim_{x \to - 2} (\frac{1}{x^{2}} + \frac{1}{x^{3} + 4})

Explain your answers using the continuity property of the addition, subtraction, multiplication, and division.

Answer 1

Given,

lim_{x \to - 2} (\frac{1}{x^{2}} + \frac{1}{x^{3} + 4})

By addition property of limits
we know

lim_{x \to a} [f (x) + g (x)]

= lim_{x \to a} f (x) + lim_{x \to a} g (x)

Therefore

lim_{x \to - 2} (\frac{1}{x^{2}} + \frac{1}{x^{3} + 4}) = lim_{x \to - 2} \frac{1}{x^{2}} + lim_{x \to - 2} \frac{1}{x^{3} + 4}

= lim_{x \to - 2} \frac{1}{x^{2}} + lim_{x \to - 2} \frac{1}{x^{3} + 4}

= \frac{1}{4} + \frac{1}{{(- 2)}^{3} + 4}

= \frac{1}{4} + \frac{1}{- 8 + 4}

= \frac{1}{4} - \frac{1}{4} = 0

Expert Answer