3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation for the tangent line to the curve at t = A/4. 3.2. Find a Cartesian equation in x and y on which this curve lies.

Q: Given y, (x) = x² is solution for the differential equation x?y" – 3xy' + 4y = 0 Using the reduction…

A: We have to find the solution of the differential equation.

Q: 4.) f(x) = etinlx)+cos (x) 2+4x+4 5.) (x) = = 6.) S(x) = +r-s)(ar-7) 622-131+7

A:

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Explanation of the answer is as follows

Q: 7. Lonsider the plane through the three polnts Po(1, 0, 0), Pi(1, 1, 0), P2(0, 1, 1). 7.1. Find an…

A:

Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

Q: Q3/ Find the limits x*+x²-2 1. lim X-1 -1 Vx+2-1 2. lim X-1 x+1

A:

Q: Without evaluating the constants, the partial fraction decomposition for 5x² – 3 f(x) (x³ – 4x²)(x²…

A: We have to solve partial fraction.

Q: Solve the differential equation dx + xdy = x?e dy. %3D

A: Given dx+xdy=x2eydyTo find solution of differential equation:

Q: 2x3 = (3xy + 1)2 Implicit Derivative with Solution and Answer

A: Given : 2x3=(3xy+1)2   To Find : Implicit derivative

Q: Decide whether the given relation defines a function, and give the domain and range. Year (x) 2005…

A:

Q: Test the series for convergence or divergence. 3 3 3 11 3 3 10 12 13 O convergent O divergent

A:

Q: Drag each set of column entrles to the correct locatlon In the matrix equation. Not all sets of…

A: This problem gives us the system of linear simultaneous equations. This system can be represented by…

Q: The solution of the ordinary differential equation -y(4) + 4y" = 0 is: O c_0+c_1 x+c_2 e^(3x)+c_3…

A: Given -y(4)+4y''=0To find solution of Ordinary Differential equation:

Q: Consider the differential equation (x- 1)y" + y' = 0. By using power series so- lution about the…

A: Please see the below picture for detailed solution.

Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. find a potential function for…

A:

Q: Given y, (x) = x? is solution for the differential equation x²y"-3xy' +4y= 0 Using the reduction of…

A:

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A:

Q: Using the Nth term test for divergence, 00 n 5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to O 5…

A:

Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A: We have to find particular solution .

Q: Given the geometric sequence where a, = 2 and r = 2 Find a10-. 32 256/2 32/2 256 O O

A:

Q: Using appropriate trigonometric substitution, dx xV4 - x2 is transformed to 1 S csc 0 de cos e d0 2…

A: Topic = Integration

Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

A:

Q: A number is chosen at random from the positive, even integers from 2 to 50. Find the probability…

A: First add the total number then add the total favorable number then use formula.

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

A:

Q: 8. Amanda invests some money for her retirement. The account pays 9%/a compounded quarterly. How…

A: I have stated the used formula in the solution

Q: can you say about the series a, in each of the following cases? |an+1 lim n- c0 (a) an absolutely…

A: We have to find the convergent test

Q: Evaluate the permutation. 5P3 60 15 125

A: We have to evaluate permutation.

Q: Determine whether the series is absolutely converger convergent or divergent. Please provide…

A:

Q: Part 4: Solve the following problem. Show your complete solution. 1.) Find the equation of the…

A: A detailed solution is given below.

Q: Show all necessary solutions. I. Find the equations of the horizontal and vertical Tangents. a. 25x?…

A:

Q: Exercise 2. Find the following limits 3x +1 1-3x² 3x +1 1) lim to 2x + 5 2) lim X+ 2x +5 3) lim x-…

A: Use limit concept

Q: The following are the critical points for the function f (x, y) = x³ Зху + уз - State what…

A:

Q: Use the graph of y = fx) shown at right to determine whether fis continuous at 0. (-6,4) 41 94) Is f…

A: We can solve this as follows:

Q: log x y = dy dx 5+5ln5logx x² In5 dy 5-5ln5log x dx x² In5 Option 4 Op tion 3 dy _ 5-5ln5logx x² In5…

A:

Q: P4: x3 (x² + 1)3

A: Use the algebraic substitution and solve the integration.

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A:

Q: solve the following first order differential equations (Homogeneous Equations)

A:

Q: Differentiate y = sin¬' (sec(4x²)) A. 8x tan(4x²) sec(4x²) y' V1 - sec2 4x² В. 8x tan(4x²) sec(4x²)…

A: Given query is to find the derivative of the expression.

Q: 17. y csc(5x)

A: Differentiation

Q: 5.1. Find the area enclosed by r = V cos(0). (Ignore the r= 2 cos(0) for this part of the problem.)…

A: 5.1) To find the area bounded by the curve r=cosθ

Q: 8- Consider u=x², v=1/u+1 and w=vv find dv/dx

A:

Q: 24 Evaluate the following. 5! 120 15 720

A: 24)  To evaluate: 5!

Q: . The population of a town reaches 113000. 7 years ago the population was 82000. Assuming that the…

A:

Q: Ql: If f(s,t) = s²t+ In(t² – s) find the value of a) atas Q2: For the following function prove that…

A:

Q: Find the differential equation of a family of circles, each having its center on the line y x and…

A:

Q: Ssec10dE

A:

Q: 2x2-3x+2 Ex(2) Let f(x) , x + 2. Find Lim f (x) x-2 x-2 Solution

A: Topic:- limits

Q: 2+ and g(x) = Figure out the domain of (fog)(x) in which f(x) = 4-x2

A: Given f(x)=2+x4-x2g(x)=1xHere…

Q: provide a step by step solution to the following equation dy/dx + 2xy + xy⁴ = 0 answer: 1/y³ = -½…

A:

Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: To eliminate the arbitrary constant.