Let C be defined by 7(t) = |cos (t), sin (2t), t²| for 0 < t < n 2 sin(Vz) 9x*dx + 2zdy + + 2y ) dz Evaluate Vz

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: (4)using the relation F= Vn show that J1(x) cos x %3D

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Q: (b) Let f(x) = sin (cos-1 (sin(cos-vx))).B f'(1) = using chain rule, show that %3D

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Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: Let f(z) = sin(3z) and C: |z| = 1. Then ſ. f(z)dz = z2(z-n)

A: In this question, we have to find the value of the complex integral by using the residue theorem.

Q: II. Let F(r) = cos(3t – 1) dt. sin x 1. Find F(0). 2. Find F'(x).

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Q: f(t) = cos(t/2) - sin(t), in the interval of [-T,1].

A: The given problem is to find the Fourier series expansion of the given periodic function with given…

Q: If f (x) = A (В B C D Stams. 0 sec²x tanx 1+1² Ite¹ 1+e tanx sec ³x 1+e -dt, then f'(x) equals tanx…

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Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: 3. Let z = x + iy. Prove that the function f (z) = e-* sin y – 10 + ie-* cos y is analytic in C AND…

A: analytic  function

Q: 3. Let G = {z = x+iy : x < 0 or y # e" sin x}. Show that G is simply connected.

A: Given: G=z=x+iy; x&lt;0 or y is not equal to ex sin x

Q: Calculus

A: see 2nd and 3rd step.

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

Q: Let F(æ) = | a cos(3t – 1) dt. sin a 1. Find F(0). 2. Find F'(x).

A: F(x)=∫sinxx2cos3t-1dtPut 3t-1=udifferentiate w.r.t t3dt=duput t=sinx then u=3sinx-1if t=x2 then…

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Let f(x) = 2x? cos(4r). %3D f'(x) = - 8x sin(4x) + 4x cos(4x) COS f'(2) = %3D f"(x) =|| 0 f"(2) =| |

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Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

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Q: Let f(x, y,2) = x² sin y+y e", where x =t +3,y = ne*-1 and z = In 2t. at t = 1 is: -2 1+2n O -12n…

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Q: Find f. f "(t) 10 cos(t) + sec2(t), -x/2 < t < z/2, f(x/3) = 5 (t) = | 10 sin (t) + tan(t) + 5 – 5v3

A: Given

Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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Q: Use the Second Fundamental Theorem of Calculus to find F"(x). F(: •¤ /1+ sin t dt t2 + 5t – 6 x /1 –…

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Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

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Q: Let f(x) = – x^3 – cos(x), po= – 1, and p,= 0, then by Secant method p2=

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Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: Verify Initial and Final value theorem for the function. f(t) = 2 + 3 cos t.

A: Given function is ft=2+3cost. We have to verify the initial and final value theorem. Initial value…

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

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Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: A. Ifw=sin(x+bt)+cos(2x+ 2bt). Prove that =6? B. If f = x*y* + 2y sinx + x²lny then show that fxy =…

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Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: Define (a) P.T. f(x) 0. (b) P.T. f(x) = x+1 [*** sin(1²) dt x 2x f(x) = cos(x²) - cos[(x + 1)²]…

A: Note: As company policy, we solve first three sub-parts only. Please resubmit the remaining…

Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: Find fy for f(x, y) = (In x) (sin x² y). O fy = (In x)(cos x²y)(2xy) O fy = (cos x2y)(x²) O fy = (In…

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Q: Given that f (x,y) = 6x2y3 - cosx + 5y2 - siny + 10x2 - e-3x ;   find  fxx ;   fyy   ; fxy ; fyx

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Q: If z=f(x,y), x= r cos θ and y= sin θ, where f is a differentiable function expressing az/ax and…

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Q: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

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Q: If F(x)=[ cos(t² +1)dt , calculate using the fundamental theorem of calculus derived version.

A: Given : F(x)=∫-xxcos(t2+1)dt Aim: to calculate using the fundamental theorem of calculus ,the…

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: If f(x) = A B C D tanx S 0 1+tan²x 1+1² Ite' -dt, then f'(x) equals 1+ e tanx In (secx)√√1+tan²x…

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Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *(;) + -1 1. 2tan () + -1 2tan…

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Q: Show that the functions ƒ 1 (x) = sin x, ƒ 2(x) : = cos x, and f 3(x)=x cos x are linearly…

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Q: 5. Given F(x) tan(t) dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

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Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

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Q: If f(x)= (A) B D plans √ 1+1² tanx I+e' f sec ³x tanx 1+tan²x Itefan 1+e -dt, then f'(x) equals…

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