Iv v and vi Determine the behavior of the functions defined below. Note that it is common to write "f(x)f(x) increases without bound - use that notation below if needed. If a limit does not exist or the function is→ " to indicateundefined, write DNE.7x3 + 8xa. Consider f(x)Complete the following equations.x2 – 7xi. lim f(x) =Previewx→0ii. lim f(x) =Preview||x→0+iii. lim f(x)Preview||iv. f(0)Previewv. lim f(x) =x→7Previewvi. lim f(x) =Previewvii. lim f(x):Previewx→7viii. f(7)Previewix. lim f(x)Previewx→00lim f(x)PreviewX.x→-00b. Based on your work in part a, on what interval(s) is f(x) continuous?PreviewWrite your answer in interval notation. If you include multiple intervals, use u to denote union.

f(x) =7x3+8xx2-7x(iv) f(0) = ?f(x) = x7x2+8x(x-7)=7x2+8x-7f(0) =0+80-7=-87⇒ f(0)=-87(v) limx→7- f(x)…

Answered: iv. f(0) = Preview v. lim f(x) =…

Math

Calculus

iv. f(0) = Preview v. lim f(x) = Preview %3D vi. lim f(x) エ→7* Preview %3D

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.6: Rational Functions

Problem 2E

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Question

Iv v and vi

Determine the behavior of the functions defined below. Note that it is common to write "f(x)
f(x) increases without bound - use that notation below if needed. If a limit does not exist or the function is
→ " to indicate
undefined, write DNE.
7x3 + 8x
a. Consider f(x)
Complete the following equations.
x2 – 7x
i. lim f(x) =
Preview
x→0
ii. lim f(x) =
Preview
||
x→0+
iii. lim f(x)
Preview
||
iv. f(0)
Preview
v. lim f(x) =
x→7
Preview
vi. lim f(x) =
Preview
vii. lim f(x):
Preview
x→7
viii. f(7)
Preview
ix. lim f(x)
Preview
x→00
lim f(x)
Preview
X.
x→-00
b. Based on your work in part a, on what interval(s) is f(x) continuous?
Preview
Write your answer in interval notation. If you include multiple intervals, use u to denote union.

Expert Solution

Step 1

$f (x) = \frac{7 x^{3} + 8 x}{x^{2} - 7 x} (i v) f (0) = ? f (x) = \frac{x (7 x^{2} + 8)}{x (x - 7)} = \frac{7 x^{2} + 8}{x - 7} f (0) = \frac{0 + 8}{0 - 7} = - \frac{8}{7} \Rightarrow f (0) = - \frac{8}{7} (v) l i m_{x \to 7^{-}} f (x) l i m_{x \to 7^{-}} \frac{7 x^{2} + 8}{x - 7} = \frac{7 {(7)}^{2} + 8}{7 - 7} = - \infty l i m_{x \to 7^{-}} f (x) = - \infty$

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