1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bogdanovich [222]
1 year ago
13

Solve 73 make sure to also define the limits in the parts a and b

Mathematics
1 answer:
Aleks04 [339]1 year ago
4 0

73.

f(x)=\frac{3x^4+3x^3-36x^2}{x^4-25x^2+144}

a)

\lim_{x\to\infty}f(x)=\lim_{x\to\infty}(\frac{3+\frac{3}{x}-\frac{36}{x^2}}{1-\frac{25}{x^2}+\frac{144}{x^4}})=3\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{3+\frac{3}{x}-\frac{36}{x^2}}{1-\frac{25}{x^2}+\frac{144}{x^4}})=3\cdot\frac{1}{2}=3

b)

Since we can't divide by zero, we need to find when:

x^4-2x^2+144=0

But before, we can factor the numerator and the denominator:

\begin{gathered} \frac{3x^2(x^2+x-12)}{x^4-25x^2+144}=\frac{3x^2((x+4)(x-3))}{(x-3)(x-3)(x+4)(x+4)} \\ so: \\ \frac{3x^2}{(x+3)(x-4)} \end{gathered}

Now, we can conclude that the vertical asymptotes are located at:

\begin{gathered} (x+3)(x-4)=0 \\ so: \\ x=-3 \\ x=4 \end{gathered}

so, for x = -3:

\lim_{x\to-3^-}f(x)=\lim_{x\to-3^-}-\frac{162}{x^4-25x^2+144}=-162(-\infty)=\infty\lim_{x\to-3^+}f(x)=\lim_{x\to-3^+}-\frac{162}{x^4-25x^2+144}=-162(\infty)=-\infty

For x = 4:

\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty

You might be interested in
10 multiplied by 1/5
Bingel [31]
10* (1/5)
= 10/5
= 2

The final answer is 2~
6 0
3 years ago
Read 2 more answers
Which point on the coordinate grid best represents the ordered pair (-5/2, -6/3)?
zhenek [66]

Answer:

point d

Step-by-step explanation:

-5/2 = -2.5 and -6/3 = -2

4 0
2 years ago
Scott wants to tip his taxi driver 20%. if his commute costs $15 what is the total cost
Vlad [161]
The total cost is $18
8 0
3 years ago
What is represented by p v q?
Stella [2.4K]
\lor is the logical or/disjunction symbol. p\lor q means "p or q". Disjunction is commutative, which means p\lor q is equivalent to q\lor p.

So if p represents x and q represents x>3, then p\lor q\equiv q\lor p means x>3 or x.

4 0
3 years ago
Add<br>(4-4i)+(3-2i)<br>Write as complex number in standard form​
Viefleur [7K]

Answer: (4-4i)+(3-2i) = 7-6i

Step-by-step explanation:

To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts. For instance, the sum of 4 -4i and 3 - 2i is 7 -6i. The numbers in standard form will be a + bi, where a is the real part and bi is the imaginary part.

8 0
3 years ago
Other questions:
  • 4 = 5x + 3y plz i need an answer for this
    8·2 answers
  • the measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147 and 130. if the two remaining angles are equal
    5·1 answer
  • What inverse<br> operation do<br> we use to get<br> the variable<br> term alone?
    11·1 answer
  • 2x+14y=-108 9x+2y= 2 Solve the following system of equations using any method
    11·1 answer
  • Jon answered 20 questions correctly on a 50-question test. Which does NOT
    13·2 answers
  • Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
    5·1 answer
  • What is 41 multiplied by 10 to the 0 power?
    8·2 answers
  • Factor the expression <br> 98x^3-50xy^298 x 3 − 50 x y 2
    11·1 answer
  • A representative sample accurately reflects a population and allows a study
    8·1 answer
  • Find the value of x. Write your answer in simplest form.<br><br><br><br> x =
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!