2 Calculate e(0) and e(0) for 1.98z E(z) = (z? – 0.9z + 0.9)(z - 0.1)

Q: 3. Find L{2t²e* cosh t}. 2 ans: g" (s+2)'

A:

Q: A potato at room temperature of 20°C is placed in an oven his temperature is 200°C. An hour later…

A: Given information: A potato at room temperature of 20°C is placed in an oven his temperature is…

Q: Solve the IVP d3 t3X(t) - 9x(t) = 18 e-3t dt x(0) =8 x'(0) = 9 x"(0) = 0 then find x(0.5) accurate…

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Q: 4.Find the temperature T (x, t) in an infinite bar if the initial temperature is 4 for |x|3. Solve…

A: Sol

Q: 3.13 Function f(x) = 3x² +6x – 5 is given. 1. Calculate the value of df/dx at x=1 using the…

A:

Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: In this question, we solve the initial value problem by using the Laplace transform and properties…

Q: Use the method of Substitution to integrate the following 5s * e^(s^2+4)

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Q: 4. Let g(x) = [ sin(r² – e*) dx. Compute gʻ(x). g'(x) = sin(x² – e") cos x 5. Let h(x) = S sin(x² –…

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Q: dx 1. Evaluate e x(In x)3

A: We’ll answer the first question that is question (1) since the exact one wasn’t specified. Please…

Q: Ax) = Ln=0 n! e Show that: GAx)dx = En=1 n(n+1) (–2)"-1 (n +2)! ||

A: Here we use integration and series theorems to find the solution.

Q: (x²-cos(2x). c. T(x) = x d. T(x) x2. find Q at x = t/4. = 100e-3x + In(4x), k=470, A= 0.01r and x=…

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Q: 23. Show that by Newton's Law of Cooling, the time required to cool an object from temperature A to…

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Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: Find the value of k that makes the antidifferentiation formula true. |(1- 10x) 1 dx=k In |1– 10x| +…

A: According to question given that ∫1-10x-1 dx=k ln1-10x+C

Q: 1) Find dy/dt for if : y = log2 (81'n 2)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: dx 1. a) Solve+ x = e-(1+last digit of your id)y 2siny. dy

A:

Q: 5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?.…

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

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Q: 2. J고dr (e* -1) (e +1)

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Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

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Q: 2. Find the general solution (4y e)

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Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: Suppose that k = 0,2hr−1 and that the smallest effective concentration is 0.04mg/ml. A single dose…

A: Given

Q: .1 Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

A:

Q: Q1 – Find dy / dx for the following functions : e0 -2 2.8ln2 Y= 4 6 * sinh 9x * Inxy sino log2 2 Q2-…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: For Problems 9 and 10, prove or disprove the following. 9. ez = ez 10. Ln z = In Z

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Q: 1 d) 2r- dz - r e² – e-z e) J ez +e-z° rp- In 3 f) 1 ez +e-z Ip-

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Q: e) S„ =E(-1)". sin (5 +n5) Vn+1 e) S. = n=0

A: Note:-  Sum of convergent and divergent series is divergent. cos2x=1-2sin2x⇒sin2x==121-cos2xput…

Q: 2) Determine the solution to the equation y' = y + x² using the following methods b.) power series

A: We have to solve given problem:

Q: Г(п + 1) (т + 1)"+1 I(n).k>0] 1 3. Show that, / (In-)" dx [Hint:/ -kx n-1 e kn

A: Question is solved.

Q: 6) x²y" – 3xy' + 5y = 0 ;yı = x² cos(ln x)

A:

Q: 2s + 5 cosh t L- s2 + 6s + 34 et 5s L-1 (s – 2)² 3t -

A: Laplace transform of the function

Q: Calculate the residue of e.e5=0

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Q: e -dx = x2 e Find c. 2 If Зе c = In 2 2 c = In(들) In(을) C e르2

A: our objective is to find the c.

Q: Solve for x(t) for the given ODE with initial values. x"(t) + 0.25x(t) = 0 with x(0)=3 and x'(0)-4

A:

Q: for the following func tion 2= 22メ - log。メ + 4"+ e?7. dx calculate differential dz when X is…

A: GivenZ=22r-log5x+4r+e27------(1)we have to calculate the differentiate dz when x is increased from…

Q: = 40 dB and By= 20 KHz is found to have N 10° K TO An amplifier with ga when T To Find T and noise…

A: Answer: For the given data,

Q: In a simple electric circuit, Ohm's law states that V=IRV=IR, where V is the voltage in volts, I is…

A: Application of derivatives

Q: Find y''of 4cos(x/2)+e^-2x

A:

Q: 3. A ceramic insulator is baked at 400o C and cooled in a room in which the temperature is 25º C.…

A: Follow the procedure given below.

Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

Q: e Lim 2. 5+s2 y4 3 Lim (4) Lipn J+ Cos늦

A: 1. lims→∞(ss+1)(s25+s2)lims→∞s×s2s×s211+1s11+5s2= 12×2=14

Q: cosh(1+ Inx)= Select one: e Inx None e?x² - 1 2xe x² +1 O 1+ 2x e?x² +1 2xe Zero

A: We will use definition of Hyperbolic function and properties of Logarithm

Q: b) Find L[e* S (-os22) dt] and -1 4s+5 * ls-1) (s+2).

A: Laplace transferom and inverse Laplace transferom, using all the properties.

Q: Evaluate L{e (cosht – sinh nt)} 3r S+3 A. (s+3)*-n² (s+3)-a² S-3 B. (s -3)- (s-3) 2. s+3 C. (s+3) +*…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.