1 Using Convolution theorem, find L' ,2 |(s² +a²)?

Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

Q: Find the Integration of: fn (3sint + esin t) cost dt In 3

A: Given that, ⇒                   y =∫π2π( 3sint +esint) costln3dt⇒                     find the value…

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

A:

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: Use the Existence and Uniquness Theorem to verify, with initial value (-2,-1): y' = xy2

A: Consider the differential equation y'=xy2 with initial condition -2,-1 Compare the differential…

Q: Integrate sin 6y sec 3y dy from limit 0 to π

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Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

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Q: ) Use integration by parts to verify the reduction cosxsin x n-1 Scos" xdx=!

A: Here I=∫cosndx ⇒I=∫cosn-1x×cosx dx using integration by part;

Q: Evaluate using integration by parts: fx sec-¹x dx

A: SOLUTION-

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

Q: п/4 sec z dz

A: By using integration formula, we calculate the given integral.

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: Solve using variation OF patometert O reductian OF order CD-+)y= secx csc x csc X

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Q: Solve by Chain Rule y = tan ( V3x² + In(5X*))

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Q: The maximum value of y = sin x, 0 &lt;= x &lt;= 2p, isand occurs at x =__________ .

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &amp;  ∆XYZ, ∠R≅∠X.

Q: Wt-1+2 dt

A: We will find the integral as following.

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Use Milne's method to obtain the value of y(0-3).

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: 3. у' %3D 2ху — х

A:

Q: The maximum value of y = cos x for - < x< is 1

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Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

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Q: The integration expression sin(3In(x)+ 4)cos(3ln(x)+ 4)dx must be transformed into using suitable…

A:

Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

Q: 5) What is the maximum value of y = 5 Cos 4x ?

A:

Q: 5. Use differentials to approximate V4 + In(1.2) correct to two (2) decimal places.

A: Let us take the function f(x)= √x f'(x)=1/(2√x) f(x+Δx)=f(x) + f'(x) . Δx   ___i) Here let us…

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

A:

Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

A: Given

Q: Y2-1 dy

A: Follow the procedure given below.

Q: he integra = 3/2 is dz Z-2

A:

Q: Find the total differential. z = 10x8y6 dz =

A: GIVEN: z = 10x8y6

Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: 4 Use Gaussian Integration (4-point form) to approximate x2sin(x)dx

A: Using 4-point formula the given integration is solved.

Q: 9. S sec³ x tan x dx

A: Given ∫sec3xtanxdx We know that  ∫secx.tanx=secx + c ∫xndx=xn+1n+1+c

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

A:

Q: Evaluate In (ax) dx using integration by parts

A: Follow the procedure given below and use simple intergation by parts.

Q: What values of a and b maximize the value of (x – x²) dx? |(Hint: Where is the integrand positive?)

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Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: 3. Approximate the integral -dx using 4 trapezoids.

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Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

A:

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

A:

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: 1 lim, „(e* + x)÷ +00

A: Explained below