Convert the Cartesian coordinate (-4,-2) to polar coordinates, 0≤ 0 < 2π r= 2√5 Enter exact value. 0 = 333 x 0

Q: Q1: A- Write the following algebraic expression in its simplest form: 5x+3x²+5x+6 X *+3 25x²-9

A: Please refer to the image below

Q: Discuss the solution on how to get the derivative of the function

A: This question is related to differentiation, We will solve it using given information.

Q: Given the points P(2, 1, 1), (0, 4, 1), R(-2, 1, 4) and S(1,5,-4)

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Q: Find the area bounded by y = 2x + x2 - x3, the x - axis, and x = -1 and x =1

A: On solving this we will get

Q: √ /1 + x² dx

A: We can solve the integration as below.

Q: Find the length of the spiraling polar curve r = 7e²0 From 0 to 2π. The length is

A: We will use the length formula of a polar curve on a given interval.

Q: (a) the volume of R using cylindrical coordinates with dV = r dz dr de w

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Q: 9) Two apartment tenants have a total of 600 feet of fencing to enclose a rectangular garden and…

A: Please refer to the image below

Q: (2xy-sinx) dx + (x² - cosy) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…

Q: dy Write down a differential equation of the form dt 11 solutions all approach y = as t → ∞. 12 y' =…

A: Given problem:-

Q: Question 6. At what value/s of x will the function y = O x = 0 O x = -3 O There is no point of…

A: Let's find inflection point of given function.

Q: QUESTION 2 Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², z(t) = lnt, t€ (-∞0, +∞0).…

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Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

Q: Use a double integral to find the volume under the plane z = 2x + y and over the rectangle R = {(x,…

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Q: √ √tan tan x dx

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Q: Find the general Solution of the following PDES Du -5X -3x = 2 +4, исx; c) = 32 + 2e du ду 3e Dx…

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Q: Consider the following vector fields: F = (3x²e²ª, 2x³e²y + 2 cos y sin y) and Ġ = (y+z, x+y, z —…

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Q: The region trapped between y 4x - 2x² and y 2x² - 1³ = y= 4х-2х² у=2х2-х3 a) Set up the integral…

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Q: (: Find the area of the region that lies in the first quadrant under the curve √x + √y = 1. (Draw…

A: The given curve: x+y=1

Q: Evaluate the Integral Sec² √r √x dr Njw SYD

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Q: Simplify csc(t) sin(t) - cot(t) to a single trig function with no fractions.

A: csct-sintcott=1-sin2tsintcot(t)=costcottcott=cost

Q: Consider the function f(x)= = x² + 7x + 12 -2 a. Find the first derivative. f'(x) = b. List any…

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Q: 4 Calculate the directed curvilinear integral I where L is the perimeter of triangle ABC with…

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Q: eiz 41. e

A: Find power series.

Q: Solve 2 cos² (w) - 7 cos(w) + 5 = 0 for all solutions. W = where Select an answer Give your answer…

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Looking for some advice on this problem please! By using derivative, determine the intervals of x…

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Q: Please answer with complete solution. Let A be the curve containing of the line segment from (0, 0)…

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Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable…

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Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: 4. Evaluate 12x+1 dx 5. Evaluate dx X 6. Evaluate [ 3x -¹ dx

A: To find the value of given integrals .

Q: convert the following differential equation into a Perfect equation and then Find its general…

A: To find the solution of the given differential equation.

Q: √x + 1 / dx X (Hint: Let x + 1 = u².)

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Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

A: Please refer to the image below

Q: A force is specified by the vector F = [(80)i + (50)j + (110)k] N. Calculate the angles made by F…

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Q: 16y¹ fit+22 (x,y) → (0,0) (b) lim (0'0) ← (¹x)

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Q: d. dx √2√x+3+x e. S da x√4x + 1 f. dx x√4x²+1

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Q: The region R is bounded by y = √x and y = x³ is revolved about the y-axis. Find the volume of the…

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Q: Solve the given initial value problem. + xy = 2 ²y² + y² = 3 O xy² + xy³ = 0 xy² − y³ = 1 O x²y² -…

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Q: An airplane takes off from an airport at sea level and its altitude (in feet) at time t (in seconds)…

A: The given equation is: h=3400lnt+1   ...1   As we know that; The Power Law: ddxxn=nxn-1 The Chain…

Q: i) n=1 1 1+2+3++n j) 1 n In n(ln(Inn)+1) k) 2" +n n!+1 n=1

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Q: Use Cartesian coordinates to evaluate SSS y² dv av where D is the tetrahedron in the first octant…

A: Given D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x +…

Q: Compute n Σ₁ tan(kx) tan((k+1)x) k=1 tan(nx) O a. + (n + 1) tan x b. tan((n+1)x) + tan x − (n +…

A: Trigonometric series

Q: con 2. 體 + dt +13y = 3sin(2t)

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Q: Use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when 0.5 ≤ x ≤…

A: We have to use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when…

Q: Apply Green's Theorem to evaluate the integral. $(3y + x)dx + (y + 5x)dy C: The circle (x - 3)² +…

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Q: sketch the graph of fox) = 2 1+x²²

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