Consider the function w = f(x,y), where %3D x = r cos 0 and Y = r sin 0 Verify each of the following.

Q: Solve the following Exact DE using Method of Grouping. 2) (y sec?x + sec x tan x)dx + (tan x + 2y)dy…

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Q: Find the PDE that is satisfied the following function u(x, t) = e' cos(x) %3D

A: Given function,  u(x, t) = et cos (x)  To find the partial differential equation.

Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: Use the Intermediate Value Theorem to show that there is a root of the equation in the given…

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Q: Use the substitution t = tan(x/2) to find the integral: 2 1+2 sin a dr Cos I

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Q: The appropriate change of variables for the dx is Vx²+2x+10 O x=10 sinØ O x+1=3 sinØ O x-1=2 tanØ O…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Given x2 + 11x + 18 f(t) = | 1+ cos? (x) At what value of t does the local max of f(t) occur?…

A: Find f'(t) using first fundamental theorem.

Q: The function f (±) = 4 cos r+ 10z has a removable discontinuity at r 0. To remove the %3D z sin z+2r…

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Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: Find the extrema of f(x) = 2 sin x − cos 2x on the interval [0, 2 ].

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Q: Given f(x,y) = 3x sin(3xy). Find fx(3,2). Give you answer correct to two %3D decimal places. Answer:

A: Topic:- partial derivatives

Q: Consider the equation below. f(x) = 2 sin x + 2 cos x 0 ≤ x ≤ 2? Find the local minimum and maximum…

A: Given,          fx=2sinx+2cosx ; 0≤x≤2π

Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: Integrate the following functions with respect to x: (1–2x)(1+ x³) (i) y = x2 (ii) y = 1+°+ sec? x…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Given sin x + cos x = 1, find x for the interval 0 sx < 2n T/2

A: Find the value of x

Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

Q: Consider the function Vx² sin? COS X - X f(x) = Vx-1 sin ++1 Determine f'(0.25) using 3 point…

A: In this question, we need to determine f'(0.25)  using 3 point central difference with h=0.01.…

Q: Sketch the following between x = 0 and x = 4 pi      y =  sin x + cos 2 x

A: Given: The function is  y =  sin x + cos 2 x

Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: Consider the following position function. r(t) = (2 sin t,2 cos t) for 0sts 2x |v(t)| =]

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Q: Let z x = 2 cos u, and y 3 sin v. Find dz in terms of u and v. %3D Provide your answer below:

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Q: Show that the function e cosy ti Siny) is an andlytic Runction 2 W= Sin Z Q2. Determine whe ther…

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Q: Iff (x) = sin x (x e R) ,then show that f is differentiable on R and f(r)= coS Y

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Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

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Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

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Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find fy(1,2,0). Leave your answer correct to two decimal…

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Q: on f(z) = e cos x+ ie-Y sin x is entire.

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Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find fx(8,9,0). Leave your answer correct to two decimal…

A: Solution

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

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

A: We know that (u·v)' = u·v' + v·u' ddxtanh-1x = 11-x2 ddxfu(x) = dfdu·dudx      (chain rule)   Given…

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: (b) Evaluate the given trigonometric integral sin r dx (x² + 1)(x² + 9)

A: The given integral is ∫-∞∞sinx(x2+1)(x2+9)dx. It is of the form ∫-∞∞f(x)g(x)sin(nx)dx. To solve this…

Q: Find the given 5x? cos 2x dx. Using this: "uv – f v du"

A: NOTE: Refresh your page if you can't see any equations. . use integration by parts take

Q: Obtain the der a) cos(xy)=2y, find y'

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Q: Find of the following functions. Do not simplify. dy da (a) y = x³ cos(Tx) (b) у (3x–10)² sin(x) Y =…

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Q: Find the tayler seris of f(x)=cos(x+pi/6) centared at a=pi/3

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Q: /2 cos a sin(sin r) dx

A: using method of substitution

Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos (50)…

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

Q: Find of the following functions: dx a) y = (x²+3x)5 b) cos(x²) + sin(y³) = 0.6

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Q: Find a function f such that ∇f = ex cos yi − ex sin yj + zk.

A: Given, ∇f = ex cos yi − ex sin yj + zk.

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.