Show that  1/3 Tn + 2/3Mn ) = S2n.

Q: sn'x プェ Sec'x-1 from [o, of 2.

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Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: VE In t dt

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Q: 3- S e J coscinx) d

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: a+, 3. f(1)=1** +a cosh /21 +bsinh /21 f(1) =2cos" (21) +e² 4.

A: The Laplace transform of the function f(t) is defined as Lf(t)=∫0∞e-stf(t)dt, since the dimension of…

Q: Show that x +2 and oe) = *+6

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Q: 2) Solve the following integral dx xV25x² – 2 V25x2

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Q: Evaluate the integral. 4π S t² sin(2t) dt

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Q: ue of the det e 16 is

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Q: 13. Find ML. J 3x + 11 K N 45 7, 10x - 12

A: According to guide and we should have been able to do only one question at a time #13

Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: 11. Jlgull sin(2t +) dt %3D e2t-3 4 4. 64e3

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Q: For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In…

A: Solution: Consider the given that; ddx∫02xlnt3+1dt We have Leibnitz Rule: ddx∫a(x)b(x)f(x,t)dt =…

Q: 10. Find the integral| dt. t* +81

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Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: 3. From Eq. (1), deduce that U2n-1 2. U2n 2. %D %3D n 2

A: 3

Q: Evaluate the integral.

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Q: Give a clear and detailed solution of the intergral of e^-ct/m 2)

A: You want intergral of e^-ct/m. I am assumig the variable of integration is "t". That is, the task in…

Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: 13. - (In t ² )º t dt

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Q: Solve for the Bernoulli DE 2t ds = s dt + 5t4s3 dt

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Q: ar integral of the c 3 – 7D2 + 7D – 2

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Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: Is there a way to solve this w/o using L'Hospital's rule?

A: Solution

Q: Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

A: These questions are related to indefinite integration, we will use use integration formulas and…

Q: find the integral of (4x − 6)5 dx; u = 4x − 6

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Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

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Q: per integral test, (-1)" A) Σ B) none of these en (-1)" dz behaves like

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Q: 1.) Evaluate In 2 e*2arctan e* 1.)J1+e2x) sec(2arctan e*)" dx

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Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

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Q: Ques tion 1 : that Given 2 x?y" + x y' + 3y= 0 show 2x* ylara) lanni)x ylurs) + (2n2.n +3) ym)-

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Q: Sa-1) CX-2xtら)

A: To find the solution of the integration.

Q: c). Invest diFrgate whether the given en equation is homogene eous dy 2. oxy

A: A first order differential equation is homogeneous when it can be written as a function of y/x, that…

Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

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Q: Find a general solution of each reducible second-order differ- ential equation y" = (y')2

A: Given, The differential equation y"=(y')2 .               ................(1)

Q: 4 In(t) dt

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Q: In GL(2, Z,,). det

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Q: Compute the integral 4x /5 – e2¤ dx. e

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Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Show that S ťe dt = 3VI

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Q: 23: Evaluate the integral of ſ (5y+7) 5 dy

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Q: dx Evaluate the given integral: S- xV5x2-4

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Q: Evaluate the integral. 7e 7t dt 7t 3+ e'

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Q: A) Vn +5 B) is larger than Vn + 5 1.

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Q: 3. (Section 4.1) Evaluate each indefinite integral. (a) /202 (b) /(3e* + 2)dr 4x (c) / (182² + 6x +…

A: We have to solve in image

Q: n²(ln(ar)) dr,a>0 J 2r In(ax) a.

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.