59. Prove the general formula 1 I x – a)(x – b) where a, b are constants such that a # b. dx In х — Ь

Q: dy +y = zy dr

A: Given equation is: xdydx+y=xy3

Q: E. Prove the following: 四- Iz.l 1.

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Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: 59. Prove the general formula iwollo oi ons dx 1 x - In x – b + C %3D (x – a)(x – b) a – b - - where…

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Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

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Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

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: Q.1) Evaluate the following integral 2dx x (3(ln z)2 + 12 In r- 15)

A: The given integral is: I=∫2 dxx3 (ln x)2+12 ln x-512

Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: Use Euler's method to obtain a four-decimal following: approximation for t (4 y=2Xy, yC)=1; yU5) =?…

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Q: If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y)…

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Q: 2. If z = x° In 2.xy, find at 1,-

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Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: (c) Prove that 00 eiz = 0. (x+i)3

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: 18. y = (In 0)" > dy de = T(In 0)-1) () T(In 6)(-1) %3D

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Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: 2m 28. t sin 2t dt

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Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: x 3*dx Jo

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Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

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Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

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Q: 2. 36 +x* dx =)

A: We have to solve

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

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Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

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Q: z'e? dz

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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: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: 4 In GL(2,Z13), det 1 4

A: We have to find the determinant using GL(2,Z13) That is, instead of usual addition and…

Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: (4z + 5)² tan zy= + dr Cos z

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: 2 Evaluate the definite integral Зх + 4 dx 11 5 17 17 2 ךי" יזנ 3.

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Q: 3. Express the general solution in terms of Bessel functions: z²y" + 4ry' + (x² + 2)y = 0

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Q: = 11% and E = 715, calculate the Еxample 4: If К. stock value of XYZ Ltd. for: 2) r= 11%

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Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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