Get the answer to "Evaluate the following limits. a) limx→∞(19x2+24x3) b) limx→−∞(19x2+24x3)"

Kaycee Roche

Answered question

2021-10-16

Evaluate the following limits.
a)

lim_{x \to \infty} (19 x^{2} + 24 x^{3})

lim_{x \to - \infty} (19 x^{2} + 24 x^{3})

Khribechy

Skilled2021-10-17Added 100 answers

Find the limits using limit properties:
a)

lim_{x \to \infty} (19 x^{2} + 24 x^{3}) = lim_{x \to \infty} (19 x^{2}) + lim_{x \to \infty} (24 x^{3})

= 19 (lim_{x \to \infty} x^{2}) + 24 (lim_{x \to \infty} x^{3})

= 19 (\infty) + 24 (\infty)

= \infty

lim_{x \to - \infty} (19 x^{2} + 24 x^{3}) = lim_{x \to - \infty} x^{3} (\frac{19}{x} + 24)

= lim_{x \to - \infty} x^{3} (19 \frac{1}{lim_{x \to - \infty} x} + 24)

= lim_{x \to - \infty} x^{3} (19 (0) + 24)

= - \infty

Therefore,
a)

lim_{x \to \infty} (19 x^{2} + 24 x^{3}) = \infty

lim_{x \to - \infty} (19 x^{2} + 24 x^{3}) = - \infty

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?