2. LetG = (Z12,) & H =< 4 >= {4,8,0}. Then [G:H]=3. *True *False

Q: If k € R+, which of the following expressions or triple integrals is NOT equal to the volume of a…

A: Option b is not true

Q: 7. Express 55C14 + 54C14 +54C15 as a single term from Pascal's triangle.

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Q: 8. The vector field F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 3z²)k is conservative. Find a potential…

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Q: Consider the conditional/implication "If pancakes are fluffy and waffles are crunchy, then bread…

A: Statement:- if p then then q Converse :- if q then p Given statement :-"If pancakes are fluffy and…

Q: 3. Integrate numerically the given function, f(5+ 3sinx) dx using (a) single application of the…

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Q: (h) be the function of two variables (a) If, in addition, x=r cost and y=r sint, find the value of…

A: 'f' is a function of two variables such that ∇→f(x, y)=3x2-3y, -3x+3y2 f(2, 1)=4

Q: Find all values of the full power. ASAP 2 (ei)√₂

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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line…

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Q: For all x € R, it is known that 1. Find the value of f(2022) (0). f()=xe +∞ 3" (n + 1) n! 2. Find…

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Q: Define the force field ₹(x, y, z) =. Let S be the portion of the plane z = 2 - 2x in the first…

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Q: 3. Use Stokes' theorem to evaluate the integral F. dr where C is the curve given by the intersection…

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Q: (a) Consider coordinates in the XY-plane, (x, y) with x, y ≥ 0 and a binary relation where (x1, y₁)…

A: Given: Consider coordinates in the XY-plane, x,y with x,y≥0 and a binary relation ≺ where…

Q: Define f (x,y) = 3y √1+x4 a. Find the rate of change of f at the point (-1, 1) along the direction .…

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Q: Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine…

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Q: Which of the following represent the volume of the solid cut of the sphere z² + r² = 16 by the…

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Q: A ferris wheel has a diameter of 24 metres. The bottom of the wheel is 2 metres above the ground.…

A: Given:  The diameter of the wheel is 24 meters. The wheel's bottom is 2 meter above from the ground.…

Q: Define the force field F(x, y, z) = . a. Find the divergence and curl of F. b. Let C be the directed…

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.43)(1z^2+9z+11 / z)dz  where C:|z|=1  Use FOUR…

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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (−1, −1) to (0, 0), C₂ is the line…

A:

Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line…

A: This is a problem on Green's Theorem. The problem has been solved step by step. See the solution.

Q: which represented quadrilateral will be classifeied as strickly a kite?

A: A quadrilateral considered as a kite if it is symmetric about its main diagonal, the two diagonals…

Q: For any two rationals a//b and c//d where a, b, c, d not equal to 0 ∈ Z, the product is given by…

A: The given statement is " For any two rational a//b and c//d where a, b, c, d not equal to 0 ∈ Z, the…

Q: A curve C is given parametrically by x = cos(t) - 2 and y = sin(t) + 3, where 0 ≤t≤ 2π Find and…

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Q: X. Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1,-1) to (0,0), C₂ is the line segment…

A:

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

A: a. Suppose,  F=∇fF=∂f∂x,∂f∂y So, ∂f∂x=12x+2+tan-1y∂f∂y=x1+y2+3y2 Now, ∂f∂x=12x+2+tan-1y Integrate…

Q: Test the series for convergence or divergence. 00 (5n - 4) 7n + 4 Σ(-1)" n = 1 Evaluate the…

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Q: +∞ If f(x) = (x-2)¹" √n-1 O O O 1-2 n=2 V +00 Σ(-1) ¹(2-2)-1 n=2 √n-1 n(x-2) ¹√n-1 +00 -n(2-2)√√n-1…

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Q: Given a piecewise function f(x) = 2, 2x² + 2x X log₂ (x-1), x < -2 -2 < x < 2, x‡0 x ≥ 2. 1. Sketch…

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Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

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Q: (10) Prove that for any prime number P>3. p² = 1 (mod 24) (Hint: chinese remainder theorem tells us…

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Q: or all x ER, it is known that Find the value of ƒ (2022) (0). Find the exact value of f(x) = +∞ 3n…

A: For all x∈ℝ f(x)=xe-x=∑n=0∞(-1)nxn+1n!

Q: Using the rule of sign evaluate e - वय x (a- Differentiation under Integral 1 +1 e-9x) dx x x

A: Note: In the question it has to be ∫0∞e-xxa - 1x + 1xe-ax dx, otherwise the question will not be…

Q: Show that the lim (x,y) → (0,0) √16x² + 9y¹² 4x² + 3y6 does not exist.

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Q: function. Write f(x) = cos(asin-'(x)}) as a polynomial function, then graph the

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Q: Which of the following is NOT TRUE about the sequence O It is increasing. O 0 is a lower bound of…

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Q: Use the Bisection method to approximate the root of the function f(x) = x³ - 7x² + 14x-6, [0,1] and…

A: We need to determine the root of f(x)=x3-7x2+14x-6 in the domain: 0, 1 using the Bisection method…

Q: Let f be a function of two variables such that and f(2,1)= 4. f(x, y) = a. If, in addition, x=r cos…

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Q: Compute the orthogonal projection of point A coordinates (2,0) onto the Set M (the closed unit disk…

A: I have given the answer in the next step. Hope you understand that

Q: √3 √√3-1² - TV I = -√√3. 2 4-1²-y² 2y dz dy dr

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Q: Let A E Cmxn and be Cm. Show that the following three statements are equivalent: . There exists a…

A: As per the question we are given 3 different statements about the matrix A ∈ Cm×n and the vector b ∈…

Q: Which of the following represents the volume of the solid in the first octant bounded by the…

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Q: Given f''(x) = = (5) Find f = - - 16 sin(4x) and f'(0) = 6 and f(0) = = - 5.

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Q: What is the equation of the tangent plane to the surface y = eª cos (z) at the point (1, e, 0)?

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Q: If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y,…

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Q: Question 30 +∞ The interval of convergence of (-1)" is x²n (2n)! 0 (-∞, 3) ○ (0,2) O None of the…

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Q: Find the Fourier series for the following functions: f(t)= |sin t], -π <t<n and The function is odd…

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Q: 7. Let G be a group. Then Z(G) is always of smaller size than G. *True *False

A: We know that ZG=a∈G  ag=ga ∀ g∈G which means that ZG is the set of those elements of the group G…

Q: Find and sketch the domain of f(x,y)=√1 - (x + 1)² − y² + 2 ln(x − y + 1) -

A: We need to determine and graph the domain for the function: f(x, y)=1-x+12-y2+2lnx-y+1.

Q: (ii) Let K={(), (1 2), (3 4), (5 6), (1 2)(34), (1 2) (5 6), (3 4) (5 6), (1 2)(3 4)(5 6)} with the…

A: