(A) Evaluate" [(x² + y)dx + (x+1+d along the path ABCA shown in figure C(0,3) A(0,1) x=3sint y=3cost ) (³4/5 -/-)

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: Compute the Laplace transform of f(t) = u(t -3) e-i2t from its definition.  (Here u is the unit…

A: We have given function is f(t) = u(t -3) e-2it The given unit step function is u(t-3) This implies…

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

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Q: (1,2) 6. Evaluate 0,1 (x²-y) dx + (y² +x) dy along a straight line from (0,1) to (1,1) and then from…

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Q: (b) (2, -5π/6) (r, 0) = (r, 8) = y -1 -2 -3 -5 -1.5 (r> 0) ] ) (r< 0) 1 -1.0 2 3 -0.5 4 y -0.2 -0.4…

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Q: b) Find all the analytic functions for which Rez = Im f(z)

A: b) A function f(z) is said to be an analytic function at any point z=a if f(z) is differentiable not…

Q: 2 - Jx - 3 – v 4) lím エ→7 x² – 49

A: Given: ⇒limx→72-x-3x2-49

Q: In x /1+ (In x)² -dp-

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Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: In (ax-1)dx

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Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: + x(x*+ zy² + ig) dy= luy) dy 2. 2. 2) 3(x y) dx -

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Compute 1 (x² + 1)(x² + 4) Lo -dx.

A: Given ∫-∞∞1( x2 + 1 )( x2 + 4 )dx

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

A: Given,

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f (1) = 1, f (2) = 1, and f (3) =…

A: The given data  is x0=1 , x1=2 , x2=3 and fx0=1 , fx1=1 , fx2=0. The spline polynomial will consist…

Q: 2) Given f(x) = ax²+bx+c has a y-intercept equal to 5, ƒ"(1)= 16, and (1,11) is a point on the…

A: f(x)=ax2+bx+cy intercept is 5f''(1)=16(1,11) is a point on the curve d dx(xn)=nxn-1

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: nd f(3x²+2y)dx- (x+3cos y)dy through the parallelogram with vertices (0;0), (2;0), (3;1) and

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Q: 5. If f (x) = (x + 1)(x2 – 2)3 then f'(x) da व्य 2= 2x (1) 2 A. & 6xx2 – 2)2 انی + (22 21 2 = Alv 3x…

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

Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: In the given y = ,what is its! 2x2 +3 dy ? x+1 2x2-х-3 a) (x+1)(x+1) dx 6x2+4x+3 b) (x+1)(x+1)…

A: Ans :  To solve this question, we will differentiate the given function y with respect to x using…

Q: If (2xy?+4) dx +2 (x*y-3) dy = 0 then ƏP/ay # ƏQ/ax *

A: Given: The equation is, 2xy2+4dx+2x2y-3dy=0 And ∂P∂y≠∂Q∂x To find: Whether it is true or false.…

Q: 2 Sketch the level curve of the function f(x, y) = y - x² for c = -2,0,2.

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Q: nd

A: Find dydx, for y=ln(tet), x=etan-1(2t)

Q: (-y dx + xdy) = (a) d(xy) (b) d(y/x) (c) d{ In(xy) } (d) -d(x/y)

A: By quotient rule , duv = v du-u dvv2

Q: In the xy-plane, the line tangent to the graph of 2 x² + xy + y² = 3 at the point (1, 1) has a slope…

A: Given equation is  x2+xy+y2=3  we need to find slope of the graph at (1,1)

Q: waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan”…

A: We will evaluate the given integral as shown below

Q: С) хdy-у vdx-x²y°dy=0

A:

Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

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Q: 2 1) (-2xy) dx + ( Sing-x²) dy

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,

Q: If y = (1 + x)(1 + x²)(1+x*)....(1 + x* ) then at x = 0 is - dx

A: Introduction :