Question

What is the end behavior of y as x goes to infinity in the equation y=-2x^3

Answer 1

Step-by-step explanation

Calculus / Limit

In this problem, we must find the end behaviour of y as x tends to infinity in the equation:

`y=-2x^3.`

• Taking the limit for x → -∞, we have:

`\lim_(x\to-\infty)(-2x^3)=-2\lim_(x\to-\infty)(x^3)=-2\cdot(\lim_(x\to-\infty)x)^3=-2\cdot(-\infty)^3=-2\cdot(-\infty)=+\infty.`

• Taking the limit for x → +∞, we have:

`\lim_(x\to+\infty)(-2x^3)=-2\lim_(x\to+\infty)(x^3)=-2\cdot(\lim_(x\to+\infty)x)^3=-2\cdot(+\infty)^3=-2\cdot(+\infty)=-\infty.`Answer

• When x → -∞, the function y tends to +∞

• When x → +∞, the function y tends to -∞