Q1. Fill in the blank with a suitable mathematical expression. 1. The function f(x) is symmetric about the origin if, 2. The yectors T and v are perpendicular if 3.Let F(x) = (2x³y)i+ (y?e#)j- (5x cos z )k then divergence o %3D

Q: Use transformations to graph the function. 34) y = sin (x – T) Ismatals adi enon ( TC 2n 3T -2+ -4-

A: Solution: Given data, y = sin(x-π)

Q: Q3:- Verify that the following functions u are harmonic, and in each case give a conjugate harmonic…

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Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: Which of the following pair of functions linearly independent

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Q: 2. Determine whether these are well-defined functions. Explain. 3 (a) f:R → R, where f(x) = x² + 5°…

A: We have to determine whether the given functions are well-defined.

Q: Ət A. Use the chain rule to find and as functions of x, y, s and t. Ət = მა Suppose z = = B. Find…

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: Which of the following pair of functions is linearly independent? (a) e, e(*-3) (b) 4, sin2x+ cos2x…

A: Which of the following pair of functions is linearly independent?

Q: 3) Find the function of y = 1) Reflect about the (2) Shift up (3) Shift X-axis 8 Units left 7units

A: The given function is y=x1) Reflect about x-axis2) shift up 8 units3) shift left 7 units

Q: Evaluate this function of z = cos x sin y; x = u – v, y= u² + v². Use chain - dz rule to find ди А.…

A: The given function are z=cosx siny; x=u-v, y=u2+v2.   Rewrite the given the function as follows.…

Q: 5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x,y), the…

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Q: 2. Determine whether these are well-defined functions. Explain. 3 (a) f:R → R, where f(x) = 2² + 5°…

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Q: . 4. Find y as a function of x if x?y" – 7æy + 16y = 0, 2. || y(1) = -5, y'(1) = -4.

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Q: Show that the function u = In(X² + Y2) is harmonic and find the conjugate harmonic v.

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Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

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Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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Q: Either f,g,h € F(R, R) the functions f(x) = sin(x)^2 And g(x) = cos(x) and h(x) = sin(x). Show that…

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Q: Find the analytic function f(z) = u + iv if u = 2 cos x .cosh 2y cos 2x + cosh 2y

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Q: Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan…

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Q: 8. Let ƒ(x) = = 21/1/2 a) (fog)(x) c) (ƒoƒ)(x) and g(x)= 3x+1, find the following: b) (gof)(x) d)…

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