contestada

What is the limit of the function?

f(x)=4x8−3x7+2x−11

Select True or False for each statement.

Limit statement True False
limx→−∞f(x)=∞
limx→∞f(x)=−∞

What is the limit of the function fx4x83x72x11 Select True or False for each statement Limit statement True False limxfx limxfx class=

Respuesta :

altavistard

Answer:

Step-by-step explanation:

The function in question is f(x) = 4x^8 - 3x^7 + 2x - 11.  The 4x^8 term is the dominant one when we focus on limits at plus or minus infinity.  For all practical terms this f(x) is f(x) = 4x^8, an even power of x.

Limit statement #1:  limx→−∞f(x)=∞ looks like 4(−∞)^8, which works out to +∞.  The first limit statement is thus true.

Limit statement #2:  limx→−∞f(x)=∞ looks like 4(∞)^8, which works out to +∞

The second limit statement is thus false.

The true and false statements concerning the limit of the function [tex]f(x) = 4x^8 - 3x^7 + 2x - 11[/tex] is:

[tex]\lim_{x \to \infty} f(x) = \infty (True)\\\lim_{x \to \infty} f(x) = -\infty (False)[/tex]

The given function is:

[tex]f(x) = 4x^8 - 3x^7 + 2x - 11[/tex]

To find [tex]\lim_{x \to -\infty} f(x)[/tex] , substitute [tex]x = -\infty[/tex] into f(x)

[tex]\lim_{x \to -\infty} f(x) = 4(-\infty)^8- 3(-\infty)^7 + 2(-\infty) - 11\\\\\lim_{x \to \infty} f(x) = 4(\infty) - 3(-\infty) -2(\infty) - 11\\\\\lim_{x \to \infty} f(x) = \infty +\infty - \infty - 11\\\\\lim_{x \to \infty} f(x) = \infty - 11\\\\\lim_{x \to \infty} f(x) = \infty[/tex]

To find [tex]\lim_{x \to \infty} f(x)[/tex] , substitute [tex]x = \infty[/tex] into f(x)

[tex]\lim_{x \to \infty} f(x) = 4(\infty)^8- 3(\infty)^7 + 2(\infty) - 11\\\\\lim_{x \to \infty} f(x) = 4(\infty) - 3(\infty) + 2(\infty) - 11\\\\\lim_{x \to \infty} f(x) = \infty - \infty + \infty - 11\\\\\lim_{x \to \infty} f(x) = \infty = \infty - 11\\\\\lim_{x \to \infty} f(x) = \infty[/tex]

Therefore:

For [tex]f(x) = 4x^8 - 3x^7 + 2x - 11[/tex]

[tex]\lim_{x \to \infty} f(x) = \infty (True)\\\lim_{x \to \infty} f(x) = -\infty (False)[/tex]

Learn more here: https://brainly.com/question/20512128

Otras preguntas