n! Show that L{e at"}(s) = - in two ways. (s - a)n+1 (a) Use the translation property for F(s). dn (b) Use the formula L{1"f(t)} (s) = ( – 1)n- (L{f}(s)). dsn

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Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: Discuss limit(n →∞)fn on B and C for  fn(x)=x/n; B=E1; C = [a, b] ⊂ E1 fn(x)=(cos x + nx)/n; B=E1

A: Note: Since you have not mention anything about the set E1, We are considering it any sunset of real…

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Q: 4. Determine exact values of 0 if 0 < 0s 2n given that tano - V3. Explain your process.

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Q: the Following is divergent

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Q: solve using reduction of order (D^2+1)y=tanx

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Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

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Q: a)Evaluate y at position x=0.5  b)Evaluate the derivative dy/dx at position x=0.5. c)Using your…

A: For a given function of a single variable, its derivative represents at which rate the function is…

Q: 2. Find the principal value using De Moivre's Theorem: |20 3 2ez

A: We know that,  eiθ=cosθ+isinθ De-Moivure's theorem:  cosθ+isinθn=cosnθ+isinnθ

Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

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Q: 2. Find the root of f(x) = 2* +x³ – x = 0 by using Newton Raphson method with initial value po= -1,5…

A: Consider the provided question, fx=2x+x3-xWith initial value p0=-1.5  and…

Q: 2. The graph of y = cosh a is (a) concave up on its entire domain because y" = coshr > 0 for all r €…

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Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2…

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Q: A homogeneous string is stretched and its ends are at x = 0 and x 1. Motion is started by displacing…

A: The boundary conditions are y(0,t) = y(l,t) = 0 and initial conditions are y(x,0) = μ0sinπxl and…

Q: A stretched string of length 20 cm is set oscillating by displacing it midpoint from the rest…

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Q: The height of a ball t seconds after it is thrown upward from a height of 7 feet and with an initial…

A: Please see the explanation below

Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: 2. Use three digits rounding to find the second approximation p, of f'(x) = x - e* = 0, by Newton's…

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: . Find the polynominal of degree 9 centered at 0 that best approximates f(x) =ln(x3+5) b. Now use…

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Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

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Q: ) A Cylinder tank of radius 4m and height 10m is initially filled with water. At the bottom of the…

A: Given that radius of a Cylinder tank is 4 meters and Height of tank is 10 meters. A hole is at the…

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: Find convergence order and the rate of the Newton's method 2x – 5x³ + 3x² + x – 1 = 0, r = -1/2, 1

A: Given: To find the convergence order and the rate of Newton's method, f(x) = 2x4-5x3+3x2+x-1 =

Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

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Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: 4 Find the distance between u = -3and z= - 1 8

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Q: 3- Find the smallest positive root of x-e=0, correct to three decimal places, using (method of False…

A: False Position Method : An algorithm for finding roots which retains that prior estimate for which…

Q: ticle at time t assuming that x(0) = -1

A: The eigen vectors are : v1=-31 , v2=-71 The eigen values are : 7 and 5. The initial condition is…

Q: Number 8

A: first find the derivative.

Q: Əz 1 Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : 201 ди and az

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Q: Briefly discuss the origin/history of De Moivre's Theorem.

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Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: Suppose z = x2 sin y, x = 3s2 + 2t2, y = 4st. A. Use the chain rule to find az and as az as…

A: We will solve the problem applying chain rule.

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: A biochemist is testing the effect of a new bacteria on a particular bacteria growing in a petri…

A: Consider the two phases separately and write down the corresponding equation for r(t). Differentiate…

Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: Let -(x) be the Taylor polynomial of degree for the function x) = cos(x) at = 0. Suppose you…

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Q: Q6) A string of infinite length is stretched from -00 to +o0 and subjected to the following initial…

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Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these O…

A: Evaluate this integral from initial to final point.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.