|Find the average distance from the origin over all the points in the unit circular disk 2² +y? <1. Obviously, the area of the disk is T.

Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is: x2 […

A: Use trigonometric substitution,

Q: (a).x = 61, y = - 4 + 7t O (r, y) = (0,4) + «(6, 7) ai + bj = 4j + 1(6i + 7j) O (1, y) = (6, 7) +…

A: topic - equation of a line

Q: Given the series, is it convergent or divergent? (5-4(In n))" %3D2 3n (V5-In n)"

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Q: Solve the differential equation y’=xsqrt(y); y(0)=1

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Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.

Q: If the increase in the side of a square is 2%, find the change in the area of the square using…

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Q: Write the following complex numbers in the form a+ib: 5 e7 1/4 = + i 2 el7 x/6 + i 7 e'5 z/3 + i 4…

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Q: Find inside r-2 oud side r=z0s6 in find quarer. area

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Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: 2. If a function f(x) is differentiable at x-a, then function f(x) is continuous at? А. х-а В. х-х…

A: Given problems:-

Q: LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 1. (9Dª + 6D³ + D²)y = 0 2. (4Dª – 45D² – 70D – 24)y = 0

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Q: O E. The series converges for p> (Simplify your answer.)

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Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0

A: First convert it in standard form then find intigrating factor and then solve..

Q: 3. Given r = t – 1 and y = t-2t, Eliminate the parameter and write an equation in rectangular…

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Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

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Q: x< +2 dx 1. I (x – 2)(x² – 2x +2)

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Q: Find fy (x,y) if f(x.y) = (x° +y®)* fxy (X.y) = %3D

A: Topic = Derivative

Q: 4x + 1 dx Jx3 + 3x2 - 6х -36 2.

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Q: has side lengths 8, 15, and 17 as shown below. hs to find cos B, tan B, and sin B. A 15 17 C AB 8.

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Q: For the series below. (a) find the series' radlus and interval of convergence. For what values of x…

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Q: n(x – 2)" 3" (2n – 1)3 * VI. Consider the power series > n=1 a. Show that the power series converges…

A: Solving

Q: 1 Given the function g(a, b) = suppose m g(a, b) where a²b+b а 3 са b = c3 + 6d am The task is to…

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Q: 2) Solve the D.E dy + (xy – xy²)dx = 0

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Q: The antiderivative of f (x) = Ga“ + 23x – 9 is F (2) = a ln (Jæ + 3|) + b ln (Jæ|) + d In (r - 1) +C…

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Q: Consider the parallelepiped with adjacent edges u = 9i + 5j + k v = i+j+ 8k w = i+ 2j + 8k Find the…

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Q: Solve the D.E dy + (xy – xy²)dx = 0 %3D

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Q: 10n? + 18 7n2 + 16n + 21 n=1

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Q: 4. sin x dx

A: As you mentioned problem number 4 solved

Q: 4. sin x dx 2.

A: Solving question number 4

Q: хах can be solved by either algebraic subsitution or integrataion by parts. x-1 (A) True B) False

A: To determine whether the given statement is True or False.∫x dxx-1 can be solved by either algebraic…

Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is= sec ede…

A:

Q: Problem 1 (а, Find the first partial derivatives of the function f(x, y) = x²yVy + 4y2. (b) fxyx of…

A: fxx,y = ∂f∂x  ;  fy(x,y) = ∂f∂y. fxyx(x,y) = ∂∂x∂∂y∂f∂x

Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { an } n=1

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Q: Q3) Evaluate triple integral , dz dx dy.

A: Topic = Integration

Q: Using homogenous differential equation determine the particular solution of xy?dy - (x³ + y³)dx = 0…

A: differential equation

Q: ctor Calculus ints possible (ungraded) AS 2) Find the directional derivative of f(a, y, z) = x² + y…

A: Answer and explanation is given below...

Q: 22n Σ (2л — 1)". - Vn² + 1 3 n=1 Use limit comparison test to show that the given power series is…

A: Solving

Q: Calculus

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Q: Use the information given about the angle 0, 0< 0 < 2n, to find the exact value of the indicated…

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Q: 22n (2r 1)". Vn2 +1 nsider the power series n=1 1. Use alternating series test to show that the…

A: Given series ∑n=1∞  22nn2+13  (2x-1)n

Q: the Q2, Find hergth of o polor Curve ア= B4 Use this formula dr de

A: Given:  The polar curve is given byr=eθ2 To Find:  To find the length of the given polar curve by…

Q: Solve for the general solution of the following differential equation and determine whether it is…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Determine if the given series is convergent or divergent. 3" en – 2" n=1 2.

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Q: E. Consider two functions f and g on [0, 7] such that I f(x) dr = 9, g(x) dr = 6, (2) dr = = 4, |…

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Q: 2. Use integration by parts to evaluate the following. (a) S x tan-x dx

A: Given

Q: Given the following heat equation and the boundary and initial conditions, и, 3 би,и, и(0,1) 3…

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Q: Reverse order, then integrate SaE ) dydx. Vx \1+

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