If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3 С. -1. D. 0.5.

Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

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Q: A new type of bacteria is found in a sample of food. Suppose P(t) denotes the population size of the…

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Q: Solve the given initial-value problem by finding, as in Example 4 of Section 2.4, an appropriate…

A: Given initial value problem  x2+y2-3dx=y+xydy where y0=1.

Q: The Weber-Fechner law states that if Y is the physical intensity of sound and X is the perceived…

A: From the given information, fY(y)=ye-y22, y>0 And X=klog(Y)Xk=logYeXk=Yexk*1k=dydx

Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

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Q: 23-28 Use a linear approximation (or differentials) to estimate the given number. 27. e0.1

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Q: The linear approximation of e is

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Q: A series circuit consists of a resistor with R = 20 Q, a capacitor with C = 0.01 F, and a decaying…

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Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: Solve the solution of the DE of the Gompertz function: dP = c ln| dt In[P

A: To solve the given Differential Equations.

Q: Question 7 - Using a suitable linearization to approximate √101 show that the approximate value is…

A: Given, 101 we have to approximate it by using linearization.

Q: Write the corresponding differential equation in time domain. F(s) X(s) s³ + 11s² + 12s + 18 s+3…

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Q: X (4) is a WSS process with E [X (t)]=2 and Ryx (T) = 4 + e- 0.1 la, Find the mean 1 and variance of…

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Q: Question 3. Prove that L(e^)(«) = * & dt.

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Q: In one model of the changing population P(t) of a community, it is assumed that = - , where and are…

A: According to question, dPdt = dBdt-dDdt

Q: A ball is thrown upwards then falls back down to the ground. If h(t) represents the height of the…

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Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: Q2: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý-y=e*

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Q: f substance B, in milligrams, left after t years, given that the initial quar

A: Option of part c is A.

Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý -ye

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Q: Use linear approximation to approximate e.03 О 1.03

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Q: FIND THE GENERAL SOLUTION OF THE D.E.

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Q: . In one model of the changing population P(t) of a community, it is assumed that 4 = -, where and…

A: As we have to solve for p(t) in (a) so there is clearly  a misprint it should be dD/dt in place of…

Q: Suppose that T is to be found from the formula T = x (ey + e-y), where x and y are found to be 2 and…

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Q: A 400 - V, 10 h.p (metric), 3 - phase synchronous armature resistance and a synchronous reactance of…

A: Solution...

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: Solve the given initial-value problem by finding, as in Example 4 of Section 2.4, an appropriate…

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Q: {fn(x)}1 converges a.e. to a function f(x) to be determined.

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Q: The solution of the following logistic equation is dy - ry (7 –);y(0) k dt 15 1 -e7rt 105 y – 7k 1…

A: Given

Q: Suppose that Yt follows a stationary AR(1) model with β0 = 0 and β1 = 0.5.If Yt = 10, what is your…

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Q: Suppose X - Bernoulli (0.5) and Y ~ Exponential (2). Suppose further that X and Y are independent.…

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Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: 4. In one model of the changing population P(t) of a community, it is assumed -, where and are the…

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Q: In order to obtain a good linear approximation for In (7.4) what would a particularly useful nearby…

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Q: Solve the differential equation using the Laplace Transform, s" + 11s' + 24s = 18,

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Q: Suppose that the specific growth rate of a plant is 1%; that is, if B(t) denotes the biomass at time…

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Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

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Q: (a) If a single infectious individual enters the city at t = 0, compute the progression of the…

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Q: Ex: Find the solution of The e ditt evential equation xy? with yCi) =1 2xy 2 dy

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Q: 12. Suppose an enzyme is known to obey Michaelis-Menten kinetics, but the parameters V and K are not…

A: Given:-             Suppose an enzyme is known to obey Michaeli's-Menten kinetics, but the…

Q: The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in…

A: a) The absorbance of a solution is measured to be A=1.30±0.05, the concentration of a species in the…

Q: Solve the given initial-value problem by finding, as in Example 4 of Section 2.4, an appropriate…

A: Given problem:- Solve the given initial-value problem by finding, as in Example 4 of Section 2.4, an…

Q: Suppose we have a pendulum clock that uses a slightly damped pendulum to keep time (that is, b is…

A: At first we will derive a direct relationship between θ and m then from that we will observe how θ…

Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: dy (b) kv. A constant

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Q: Given the stochastic differential equation: dx = dt + 2/x¢dWt, x(0) = 1 What is the expectation of…

A: Given: Here the given stochastic differential equation is  dxt=dt+2xtdWt          , x(0)=x0 Where…

Q: Find the initial value of f(t), if: 2(s + 2) s(s + 1)(s + 3) F(s) = -

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Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…