1. (a) Evaluate the integral: ∫0 to 2 16 /x^2+4 dx
Your answer should be in the form kπkπ, where k is an integer. What
is the value of k?
Hint: d/dx arctan(x)=1/x^2+1
k=
(b) What is the upper bound for your error of your estimate if you
use the first 11 terms? (Use the alternating series estimation.)
=
2.
The function f(x)=8xln(1+x) is represented as a power
series
f(x)=∞∑n=0 cn x^n.
Find the specified coefficients in the power series.
c2=
c3=
c4=
c5=
c6=
Find the radius of convergence R of the series.
R=
In: Math
(1 point) Two chemicals A and B are combined to form a chemical
C. The rate of the reaction is proportional to the product of the
instantaneous amounts of A and B not converted to chemical C.
Initially there are 38 grams of A and 14 grams of B, and for each
gram of B, 1.2 grams of A is used. It has been observed that 13
grams of C is formed in 5 minutes. How much is formed in 30
minutes? What is the limiting amount of C after a long time ?
grams of C are formed in 30 minutes
grams is the limiting amount of C after a long time
In: Math
Question 4: Homogeneous Second Order Differential equation
Solve the following equation for the particular solution.
i. 2?′′ + 5?′ + 3? = 0; ?(0)=3, ?′(0)=−4
ii. 4 (?2?/??2) + 8 (??/??) + 3y = 0 ?(0)=1,
?′(0)=2
iii. ?′′ + 6?′ + 13? = 0; ?(0)=2, ?′(0)=1
In: Math
Solve the following integral ∫ (x^2 + x + 2) / (x + 1)(x^2 + 1) dx. Use partial fraction decomposition. Show all work and steps to get to solution.
In: Math
Q1) Velocity and acceleration: a ball is thrown verticality up word from the ground level with initial velocity of 2 feet per second and initial position 10 feet. Use a(t)=2cos(2x+3)
Find the equation of the velocity of the ball
After how many seconds is the velocity of the ball one
-half the initial velocity?
Find the equation of the motion of the ball
Calculate that displacement from t=1 till t=5
seconds
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Joe leaves an intersection traveling west in his car. He is 20 feet from the intersection 4 seconds later. At the same time, Joshua leaves the intersection heading north in his car so that his position 4 seconds later is 26 feet from the intersection. If, at that instant time, Joe's speed is 8 feet per second and Joshuas' speed is 12 feet per second, find the rate at which the distance between the two cars is changing to the nearest tenth.
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A bath tub with a volume of 400 liters at first is full of 100 liters of water with a bath salt concentration of 10 grams per liter. During some time, water with a bath salt concentration of .8 grams per liter starts to stream at 4 liters per minute simultaneously a leak in the tub causes the water and bath salt mix to stream out of the bath tub at the same pace. Determine the amount of time needed for the water and bath salt mix in the bath tub to be lessen to 3 grams per liter, please show all work and explanations!
In: Math
Question 3: Exact Differential Equation
i. Test to see if the following equation is exact, if exact solve
for the general solution
(??/??) +(2? ????+?^3?^?)/(?^2cos?+3?^2?^?)=0
ii. Solve (?+????)??+(?????−2?)??=0
iii. Solve (?^2+?)??+(?^?−?)??=0
iv. (2?−3?)??+(2?−3?)??=0
I am sorry I could not send a photo. Whenever I try from the app it posts another question on the same page. I tried doing them individually and the only thing that happened was that the same question got posted 4 times. I would appreciate your help in solving these. Thank you!
In: Math
use the definition of the Taylor series to find the first four nonzero terms of the series for f(x) centered at x = a
a) f(x) = xe^x, a = 0
b) f(x) = sin (x), a = π/6
In: Math
A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is released from a point 1 foot above the equilibrium position with a downward velocity of 2 ft/s.
1) Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 4 times the instantaneous velocity.
2) Classify the motion as underdamped, overdamped, or critically damped.
In: Math
we were looking at lives some men mathematicians. But women made very serious contributions to mathematics as well. One of the most important people in the history of mathematics was Emmy Noether. Please research what you can find about her life and contributions, and share a thought.
In: Math
solve completely(complementary function and particular integral) pdes
1 (1+D^2-D')z = -8siny
2 (D-D'-D'^2)z =132xy^10+504x^2y^6
3 (D^2-4DD' +4D'^2)z = x + y
4 (D^2-2DD'+ D'^2)z = e^2x-2y+x^2
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Respond to the following in a minimum of 175 words: How will you graphically represent data in your future career? What types of graphs are typically used in that industry? What types of conclusions are drawn from the graphs?
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Suppose A*B*A′ holds(B is between A and A') and D ∈ Int(∠ABC). Prove that C ∈ Int(∠A′BD).
(a) Prove that C ∈ H(D,line A′B).
(b) Prove that C ∈ H (A′, line←→BD). Use point A.
(c) Deduce that C∈Int (∠A′BD).
In: Math