Use a familiar formula from geometry to find the length of the curve described and then confirm using the definite integral. r=2sinθ, 0≤θ≤π

Q: 15. ſ sin² 3t cos 3t dt

A:

Q: Express the Cartesian coordinates (-3,1) in polar coordinates in at least two different ways. Write…

A: We have to convert in polar coordinates.

Q: Solve the equation (x^4 + 2y)dx - xdy = 0

A: I am attaching image so that you understand each and every step.

Q: Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x - 3 dx x² –…

A:

Q: (x^2)y - y^2 - x^3 = C (x^2)y + y^2 - x^3 = C (x^2)y + y^2 - x^3 = 0 (x^2)y + y^2 + x^3 = C

A:

Q: 4x + 1 - dx 4x2 + 2x + 3

A:

Q: Find the differential dy of the given function. Xx + 5 y = 2х — 9

A:

Q: taylor tan)

A:

Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 7 \" 9n2 + 5 00 n =…

A: We have to find out the series convergence test

Q: Find the 8th term, ag, for the sequence. an = - 9n +6 %3D

A: Given :an=-9n+6

Q: G(x) = Si tan t dt Find G(1) = Find G'() =

A:

Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values…

A:

Q: B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy…

A: Let's find.

Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: (x+3)° 3. Use logarithmic diffrentiation to find the derivative of y' =- (1+2}(r+4}

A:

Q: f(Tn) for For the function f(x) = tan(r), write Newton's formula as Tn+1 = F(xn) = In [(").f solving…

A: Find your answer below

Q: This matrix is a 0 0 4 0 [ 4 0 0 zero matrix square matrix diagional matrix unit matrix O

A: Given problem:-

Q: Find the volume generated by revolving the region bounded by y = - cos x and y = 0, from x= - 2x to…

A: Here, the curves y=-cos x & y=0 from x=-2π to 2π revolved about the x-axis.

Q: 2. Evaluate f]x-1dx 1 O 2 O None of these

A:

Q: items 10- 12. Ana and her mother went to the market to buy fish for their picnic. The fish that they…

A: Price , discount

Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

A:

Q: Find the vector component of v = 2i – j+ 3k along b = i + 2j + 2k and the vector component of v…

A:

Q: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: 2 4-x Find the area in the first quadrant bounded by the coordinate axes and the graph of y = 5 The…

A:

Q: Question #6 The area in square meters of a pond covered by an aigae bloom decreases exponentially…

A:

Q: Find fxy for the function f(x, y) = V3x²y + 5.

A: The given function is f(x)=sqrt(3x2y+5).

Q: The future value at 5.25% interest, compounded continuously for 7 years, of the continuous income…

A:

Q: Find the nth term of  (– 4 3 14 29 ) and (4, 5, 8, 13)

A: Sequence

Q: A variable force of 6x−2 pounds move an object along a straight line when it is x feet from the…

A: Given: Force that moves the object along straight line is 6x-2, when the object is x feet from the…

Q: ) Find of the implicit function a? + 5xy + y? – 2x + y – 6 = 0 at the point 1. . (1, 1).

A: Topic:- derivatives

Q: 9. sin ở In(cos 0) de

A: let I=∫sin θ ln(cosθ) dθ Integration By parts: ∫udu=uv-∫vdu u=ln( cosθ) ; du=1 cosθ-sinθdθ=-tanθdθ…

Q: Test the series for convergence or divergence. 4 6. 8 10 .... 7 8 10 11

A:

Q: For the differential equation (x2 – 9)y" + (x – 3)y' + 2y = 0, a regular singular point is: O x=3…

A:

Q: a) If u = 1- make i the subject of the relation. b) (*) 2. 4. 6. 8 4. 6. 2. 4. 4. 6. 2 4. 6. 8 4.…

A: Group theory

Q: Find f, and f, as functions if 2y f(x. y) = y+ y + cos x

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

Q: Solve the equation xy^3 dx + e^(x^2) dy = 0.

A:

Q: 3. he tangent to the ellipse I at the point P: V2 4. 3. 3w q(w) = 2w+ V2 %3D 3 q(w) = 3w V2w - V2 3…

A: Ellipse tangent

Q: farmer finds that if she plants 55 trees per acre, each tree will yield 35 bushels of fruit. She…

A: Given query is to find the number of trees to be planted per acre.

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = 7 for f(x) = 1+z T2(x) must be of…

A:

Q: In this problem you will use variation of parameters to solve the nonhomogeneous equation t'y+…

A:

Q: Solve the equation .11 y" + 3y' + 2y = x2

A:

Q: f (x) = arctan(x) Consider Using the given f (0.75) by making use of function at approximate the…

A: This is a problem related to series expansion. Based on the general formula and concept we will…

Q: Q2) Find the volume of the solid generated by revolving the "tri- angular" region bounded by the…

A: Washer method: To find the volume enclosed between two functions, the washer method is applied. We…

Q: A mountain climber is about to haul up a 70-m length of hanging rope. How much work will it take if…

A:

Q: Sketch the graph of an example of a function f that satisfies all of the given conditions. f(x) = 4,…

A:

Q: Let Sx² + 3 f(x) = l(x - 2)2 if x 2 1° if x < 1 (a) Find the following limits. (If an answer does…

A:

Q: [2 1] and B= 3 2, then (AB)T is equal If A = 10 -2 7 Option 2 None of these -3 7 -3 -2 10 2 10 7…

A: Given

Q: 8. 3. xp-

A:

Q: 53. If sin (t) = -! and t is in the 3rd quadrant find cos(t)

A:

Q: * The solution of the differential equation below is dy = ky dx %3D x = eky y = ekx Option 2 O…

A: