4) The inverse of y In a2 is: a) x = a" .b) x = a²y, c) y = a* . d) y = ax 5) the derivative of 5tan 2x is: a) sec 2x 5lan 2x, b) 2sec? 2x 5tan 2x d)2sec 2x In 5 5tan 2x c) sec 2x In 5 5tan 2x 6) The derivative of exy-10 a) e-(49) , b)(1+ e*y) , c) (e-t) - 1) , d) none of them

Q: If u=f(x2+2yz,y2+2zx).Prove that

A: Given: u=fx2+2yz, y2+2zx Let u=fv, w where v=x2+2yz and w= y2+2zx. Now prove…

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

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Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

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Q: The convolution of e2t ® sin(3t) S is | e2Usin(3t – 3u)du e2usin(3t – 3u)du Se-2usin(30)du…

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Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: y If z = show that = 0. x + y?*

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Q: If h(x) — За — — 1, j(x) k(x) = 21x? – 26x – 11 , show - 7x + 11 , and - - - - h(x) · j(x) = k(x).

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Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

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Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: gion enclosed by y

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Q: An ODE is said to be stable is every arbitrary constant on its solution, such as C1 and C2 for…

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: 3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then…

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Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: 74. Show that if 0 < x < y, then Vỹ - Vx < Vy – x.

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Q: 9. Prove (1, sin z, cos z} is linearly independent in [0, 2x].

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Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: 1. Show that sinz is unbounded on C and lyl <|sinz] <ebl z=x+yi € C. for

A: Given:         We have to show that sinz is unbounded in ℂ and y≤sinz≤ey   for z=x+yi ∈ℂ Function…

Q: Prove that d (sec"x)= 1.

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

A: 3

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

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Q: If y = xsinx then prove that y''+y=2cosx

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Q: 6) MLATU = 45°, mZSTU = 120x – 1, and mZSTA = 73x + 1. Find x. %3D %3D T. U A

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Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: Use Greens Theorem to evalute fyx² dx + x²dy as shown below Leh Half of (0,5) +y-25 (0,-5)

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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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: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: Suppose csc(4) = 2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D

A: Given that                                     we have to find value of…

Q: If x<y, prove that x<(x+y)/2<y?

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Q: dual of c, is isometric to l'.

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Q: If In(ax)dx = 2, then a = %3D 1

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Q: J sec° (10t) tan“ (10r) dt 4 10.

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Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: 2 la), Pu (aw by Re currence relation

A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Consider i = (1,0,0), j= (0, 1, 0), k = (0,0, 1) and, f (x, y) = (x, ²y°, sin x, cos y, xyean +3…

A: We have to make the appropriate selection  With the help of following transformation-

Q: "(2) is also analytic, and hence its

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A: Given that, f1(x)= x, f2(x) =cos2x and interval is [0, 90o] Wehave to find that the functions are…

Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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Q: 3. Gien that F cxy) = s Can servative find putantial -> functin fo Ě a

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