Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

Q: 3. A plastic of warm water with a temperature of 110°F is placed inside a 0°F freezer. After 20…

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Q: A population of insects increases at a rate of 200 + l0t + 0.25t 2 insects per day (t in days). Find…

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Q: Find the integral of (e^x - 1)/(e^x + 1) dx.

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Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: What is the amount of salt in the tank at time t = 0?

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Q: (8) dx Compared to I dx x In|x| Conterges or Diverges

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Q: 2 S (x) + x³)dx = ? -1

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Q: Evaluate dx dy in y=cosh(in e") b. 3x sinh (In x') 3x² sinh(In e* ) d. 3x sinh (3x² ) с. a. 3x…

A: Given:     y = cosh ( ln ex^3 )

Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: Suppose the quantity (in grams) of a radioactive substance present at time t isQ(t) =…

A: Radioactive substances have different rates of decomposition.

Q: dN The rate of the growth of species of bacteria is estimated by = 800 + et dt Where Nis the number…

A: Given function is form of differential equation. we will integrate this function to get the N(t).

Q: A 200-gal tank is half full of distilled water. At time t = 0, a solution containing 0.5 lb /gal of…

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

Q: Find the rate of change of x with respect to p. 4 x2 0 0.000001x2 + 0.09x + 5 dx dp ||

A: Proceed as shown below

Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: valuate the indefinite integral. 7 dt (t + 1)?

A: Given query is to eveluate the integral.

Q: A cola vending company estimates that their cola will be consumed by people at a rate given by: C…

A: Topic = Algebra

Q: 5. Suppose that f(t) is the rate of snowfall t hours after midnight on December 21, measured in r12…

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Q: Evaluate the integral. | (e7* +3e -x) dx 7X +3 e -X) dx=

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Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

A: As per bartleby guidelines we only give first question answers.

Q: 1. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

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Q: Suppose that the population P of mussels in Lake Erie t months after January 612 2015 is given by…

A: Given: The population P of mussels in Lake Erie t months after January 2015 is given by Pt=6t26t+8.…

Q: Show that the value of Vx + 8 dx lies between 2V2 - 2.8 and 3.

A: According to the question, we have to prove that the value of integral ∫01x+8 dx lies between 2.8…

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

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Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: Find e dx approximately using Simpsons rule with n 10.

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Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: 12 1 dx using a left-hand sum with n = 3. Estimate

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Q: valuate the following integral: x2 + 5x + 6 dx. J ( – 1) (x2 + 3) |-

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Q: Jrin m In(cos m) dm

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Q: A 13-g sample of radioactive iodine decays in such a way that the mass remaining after t days is…

A: Given , 13gm of radioactive iodine decays in auch a way that the mass remaining after t days is…

Q: e2x 2.) S. dx ex – 5

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Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

Q: Q3/ Find the integral x e* dx by using trapezoidal and simpson methods with an error of no more that…

A: According to question given :Integral ∫01x ex dx by using trapezoidal and simpson 38 methods with An…

Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: 37. What is the value of the given integral? dt |(-log,t) o VIT • None of these o -VT 2

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Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

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Q: log3 (cosh a) + csch x) tanh x dx

A: Given: To evaluate the given integral to find its antiderivativeand to reverse the process to verify…

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: find the antiderivative of dx/sqrt(ex-1)

A: To find : The antiderivative of dxex-1 Solution The antiderivative can be evaluated as, ∫dxex-1 Put…

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

Q: Find the average rate of change of h (x) = -2x+4x from x -2 to x 1. Simplify your answer as much as…

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Q: Sõlve the integral - In 3 x'e-*dx 2.

A: The given integral ∫0ln3x2e-xdx can be evaluated as, ∫x2e-xdx=x2×∫e-xdx-∫ddxx2×∫e-xdxdx+C…

Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

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Q: Sind dy forys(x) dx 3517X

A: y=(xx)3sin x

Q: Using Simpson's method Vx dx for n=4 is equal to

A: We have to evaluate ∫01xdx for n=4.

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

A: