= [2, –3, 0] = [ u -2u Ex: 5 :

Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

A:

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

A:

Q: aw Find ду if w = z³(In(zy))(e**y*z*) %3D

A: Given,        w=z3ln(zy)ex2y3z4

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

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

A:

Q: 2スゴ+メリ+タJ=0 condition

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Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: y z = x + show that : 0.

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Q: jn= 16, α=0.05

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Q: The functions y,(t) = sin(2t), y,(t)= cos(2t) are linearly independent on (-0, x). Select one: OTrue…

A:

Q: Find 1 2 – if | - Əx y,z w = x2 +y – z + sin t and x+у %3Dt

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Condition JW=3.6, j0=0.4

A:

Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: dy If tan(ry) + 5 = ry then show that dr? 2y

A: Differentiation two times

Q: Find ƒxx ( x, y)  and ƒxy( x, y).

A: Given, fx,y=3x+yx-1. The objective is to find fxxx,y and fxyx,y.   fxxx,y is found as follows: First…

Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

A:

Q: 1. z, =1-j2 and Z,=2+j3; Evaluate cos[Z,J?

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

A:

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: 2+i Evaluate (2x+1+iy)dz along (1-i) to (2+i) 1-i

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Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: Z. tan X= u CosV, usinv y: find 23 and >Z

A: Given, x = u cosv, y = u sinv, and z = tan-1 x/y, we have to find the partial derivatives of z with…

Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

A: Solution:-

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

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: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: •1-i Evaluate 4z dz . J3i

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Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: 2 2xy) dy, v es (0, 0), (2, 0), (

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Q: - Find + Uy, Given that u(X,y) tan(x+11XY+y")

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Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3 and ajj = i. j. Th

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Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

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Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

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Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

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Q: If z = 1+ eie Find z*, z?.

A: Conjugate of a complex numberz is formed of same real part and opposite imaginary part. Its…

Q: - gt V Xu u = (1,3,-3) , v = (4,0,2) e l

A: The given vectors are: u=(1, 3, -3)v=(4, 0, 2)

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.