The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in Cartesian form is defined by

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Q: Q4: Evaluate the following integral. 7/21/2 sin y 5% dy dx Y

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Q: The particular solution In (x) = 3x + 4y, y(0) = 0 is A. e³x + 3e-4y = 4 B. 4e3x3e-4y = 3 C. 4e3x +…

A: Topic = Differential equation

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A: Given, ∫(x csc2 6x-x cos 6x)dx

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A: The path r(t)=4 sin ti+4 cos tj

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A: Given problem:-

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A: Two people on bikes are at the same place. One of the bikers starts riding directly north at a rate…

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A: 10.The given function gx=15x-2.3-7.4

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² -…

A: Above question is solved.

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Q: Q6. Verify 02 f exDy Dyx for the function f(x, y) = x² sin2y + y²sin2x

A: A detailed solution is given below.

Q: Show that lim in(+¹) + sin(+²) + n *** + sin(2) cos(1) - cos(2).

A: Above question is solved.

Q: 2) Find the particular solution using the following indicated initial values. (D² +4D+5)y=10e³; when…

A: Given :D2+4D+5y=10e-3x

Q: 2 dydx -23-1 (xy)³ SS.

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Q: find the points at which f has a local maximum or a local minimum

A: This question can be solved using the concept of maxima and minima.

Q: en ủ × ʊ = (2, 3, 4), find (ũ − 4v) × (ũ + 3v).

A: Topic:- vector algebra

Q: Iff and g are differentiable functions and h(x) = f(x)ex) , then K'(x) = rosen Fixe+fixie O [00+0000

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Q: 5. Find the residues of the following: a. 2-2 z(1-2) at z = 0; at z = 1

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Q: To test this series for convergence n n=1 √n² +1 8 You could use the Limit Comparison Test,…

A: We will solve this question using limit comparision test.

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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Q: Find the perimeter of the triangle with ver an isosceles triangle?

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Q: Given that f(x) = (x - 2)² and g(x) = 1 - 3x, find (a) (f + g)(4)= (b) (f - g)(4)= (c) (fg)(4)= (d)…

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Q: VIP 2 = √ Бхутуг П , Ө от 58 x = CS 0 ) y = Sine -

A: Topic:- application of derivatives

Q: Q4- Solve the following differential equation: (1 + x²)dy + (y − tan−¹(x)) dx = 0 -

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² =…

A: Let's find surface area rotated about x=0.

Q: Find the length of the curve y= 2²-√√x, 4 ≤ x ≤9. 23/2 3

A: To find the length of the given curve.

Q: 2. The values of g and g' are given in Table 6. -1 Complete the columns for g¹ and (g-¹). X 1 2 3…

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Q: A 30-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

A: We have to find the limit.

Q: 3 50 times داد + 33 u س اع

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Q: A coulomb is the same as; * O Ampere.second Ο Ο Ο Ο Ampere.second^2 Ampere/second Ampere/second^2

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Q: A) Explain with short examples the algebraic vector properties. 1. A+B=B+A 2. A+ (B+C) = (A + B) + C…

A: To explain with the examples with the algebraic vector properties given.

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: 5: Evaluate I where D is the rigion bounded by xy ve x+y = 7 SS (X+Y) DA D (1

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Q: Determine whether the differential equation (2x² − 2xy + 3) dx + (7y² − x² + 2) dy = 0 is exact. If…

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Q: (d) If f'(x) = g'(x) for 0 < x < 1 then f(x) = g(x) for 0 < x < 1. True False

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Q: Express the repeating decimal as a fraction. 0.474747...

A: Let's express as a fraction.

Q: Evaluate 2 x√√x² + 4 dx.

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Q: or each function h(x), find two functions f(x) and g(x) such that h(x) = f(g(x)) a) h(x)=√x² + 3 b)…

A: Topic:- function

Q: 1. Find the power series expansion for the following functions and find its interval of convergence.…

A: Let's find power series expansion.

Q: Solve step by step in digital format (2 + x)² − 4 d) lím x-0 X 6x² - 3x + 2 e) lím x-0 4x - 3

A: Given, Evaluate,

Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A: This is  a problem related to maxima and minima of the function. Based on the general formula and…