Anonymous

Hello. I am stuck on what the formula for N(t) is. Any help to this question would be greatly appreciated. Thank you in advance!

A packet arrives at a router every T seconds with the first packet arriving at time 0. All packets require an equal γT (0 < γ < 1) seconds for transmission. If the propagation delay per packet is L seconds, then what is the total number of packets in the system N(t) at any time instance t? What is unique about N(t)? Plot N(t) against time with proper annotations.

The original function is x/x^2+9

The first derivative is (-x+9)/(x^2+9)^2

The second derivative is ???

I am having trouble finding the second derivative and simplifying it enough to eventually set its numerator equal to zero and therefore to find its inflection points.

Please help end explain the steps. The correct answers are (0,0) and (pos or neg 3 sqrt 3) and (pos or neg (sqrt 3) /12) ). I would like to learn how to get these answers.

Thank you in advance.

The examples I have been doing haven't included any fractions, and I am stumped on how to do this problem. Please explain every step as simply as possible. Thank you in advance.

Consider this function, along with its

derivative and its second derivative.

y= x / (x^2 - 4)

y'= -(x^2+4) / (x^2-4)^2

y''= -(x^2-4) 2x-4x (x^2+4) / (x^2-4)^3

A) What are the critical numbers (if any)?

B) On what intervals is the function increasing and on what intervals is the function decreasing?

C) What are the inflection points (if any)?

D) On what intervals is the function concave up and on what intervals is the function concave down?

E) What are the maxima, minima, and asymptotes?

Let f(t) = the integral with bounds from 0 to 8t of cos(x) dx.

Find df/dt.

Please explain the steps as simply as possible, as if you were teaching it an idiot who can't do math.

Thanks in advance

A particle's acceleration is given by

a(t)=12t+4 inches/second^2

The particle's initial position is 2 inches from the origin and its velocity at t=1 is 5 inches/second. What is the position of the particle at t=2?

A) 10 inches

B) 12 inches

C) 16 inches

D) 4 inches

E) 20 inches

The area of the region in the third quadrant is bounded by the graph of y=x^3. The line y= -8 and the y-axis for x between -2 and 0 is given by

A) Integral from -8 to 0 (x^3+8) dx

B) Integral from 0 to -2 (x^3+8) dx

C) Integral from 0 to -2 (x^3-8) dx

D) Integral from -8 to 0 (x^3-8) dx

E) Integral from -2 to 0 (-8 - x^3) dx

I know you have to subtract, but I'm not sure about the signs. I was told that you subtract, but since the area is under the x-axis, the two negatives make a positive and that the correct answer is B. Is that correct? I have no idea what I'm doing

Thanks in advance

If f(x) = 2+ l x - 4 l then what is f '(4)?

A) 2

B) 1

C) -1

D) 4

E) Does not exist

I found the derivative, but I don't know what to do afterwards to find f '(4). When I substitute, I get 0/0, which doesn't make sense. Please explain the steps simply as I suck at math. Thanks in advance

P S. If it helps, the derivative I got is 2(x-4) / l x - 4 l

Can someone please explain the steps so that I can do this by hand? Using a calculator I can see that the function has a vertical asymptote at 0, but how would I know that the limit does not exist without a calculator? Thanks in advance

As the limit approaches 0 (sin(5x)) / x^2

Why is the answer does not exist?

Hello, I need help completing the problem. Please explain step by step because I am confused and it helps a lot. Thank you in advance

1) Given: f(x)= sqrt (4+sin(x))

a) Find the derivative.

The derivative of f is 1/2 (4+sin(x))^-1/2 (cos(x)) dx

b) What is the linear approximation, L(x) to f(x) at x=0?

???

2) What is the approximation for f(0.1) given by using linear approximation or the method of differentials. (multiple choice)

A) 2.0246

B) 2.0248

C) 2.0250

F(x)=(2x^2-8)/(x^2-16)

Find the intervals of increasing and decreasing, local maximum and minimum values, points of inflection, and concavity.

Please explain step by step because I have the answers, but I do not know how my professor got them, and I want to understand the process. Thanks I’m advance

Find the critical numbers of the function. (Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.)

g(x) = 24x − 6 tan(x)

This is what I have so far:

g(x) = 24x − 6 tan(x)

g'(x) = 24 - sec^2(x)

g'(x) = -6 ( -4 + sec^2(x) )

I get stuck here

Please explain the steps as that is helpful. Thanks in advance

Verify the given linear approximation at a = 0. Then use a graphing calculator to determine the values of x for which the linear approximation is accurate to within 0.05. Round your answers to two decimal places. Enter your answer using interval notation.

tan(x) ≈ x

What I have so far:

f(x) = tan(x)

f '(x) = sec^2(x)

f(0) = 0

f '(0) = 1

f(x) =~ f(0) + f '(0) (x-0)

f(x) = 0 +1 (x-0)

f(x) = x

We need tan(x) - 0.05 < x < tan(x) + 0.05

This is where I get stuck. Please explain steps as it is more helpful

Thanks for your help in advance.

The correct answer is supposed to be sec(x)(1-7sec(x)) / tan^2(x), but I can't seem to figure out how my HW got that answer.

This is what I have so far:

Using the quotient rule f'(x)g(x)-g'(x)f(x) / [g(x)]^2

y'(x)=(-sec(x)tan(x))(tan(x)) - (sec^2(x)(7-sec(x)) / (tan(x))^2

This is where I get stuck. I think you're supposed to factor out sec(x), but I'm not sure how.

Thank you for your help in advance.

Proof:

Given: QRST Q(-a,a), R(0,2a), S(a,a), T(0,0)

Prove: QRST is a rhombus

A rhombus has perpendicular diagonals, and I already got 0/2a for SQ and and -2a/0 for TR. The slopes are perpendicular reciprocals of each other, so all is good for that.

The thing I'm having trouble with is its sides because I got a different answer for almost every one.

A rhombus is also supposed to have four congruent sides, so I plugged in the coordinates into the distance formula, and I got 0 for both QT and RS. Then, I got 2a squared for QR and -2a squared for ST.

Can someone please point out what I'm doing wrong because I am getting no where with this problem.

Thanks in advance.

I'm just confused on how to do this question. I already tried doing the Point -slope formula and tried putting the equation y= -2/3x + 9.7 into my graphing calculator, but then I realized that I didn't even know what I was searching for. I also tried doing the slope formula and setting it equal to -2/3, but that didn't work out for me either. I must be losing it. Isn't the slope of a vertical line undefined?

Please help. Thanks in advance.

The word equation is:

Sodium hydrogen carbonate + calcium chloride + water --> sodium chloride + calcium hydroxide + carbonic acid.

I changed them into their chemical formulas

Na(HCO3) + CaCl2 + H2O --> NaCl + Ca(OH)2 + (H2CO3)

I have been trying to balance this equation for the last twenty minutes, but I must be doing something wrong. Please help me balance the equation, and explain how you got that answer if you could.

Thank you in advance

Please help, I'm stuck on this question!

One example could be: The news often shows stories such as celebrities getting away with things such as doing drugs

^Celebrities are using the freedom they have for their own benefit.