The equation of a circle can be represented as in-h)² + (y – k)² = r², where (h. k)ie center of the circle and r is its radius. For a circle centered at (3, -1) with radius 5, y = A) -1± /25 – (x – 3)2 B) -1± /25 + (x – 3)2 C) 1+ /25 – (x – 3)² D) 1+ /25 + (x – 3)² %3D | | |

Q: Differentiate. y = In [(x + 5)5 (x + 1)6 (x + 8)²] d [In [(x + 5)(x + 1)®(x+ 8)²]] = O dx

A: Given:- To differentiate:-

Q: graph of flx)= Inlx) concave down 7

A:

Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: If Arctan gx 3. dx =b Arctan* 3x +C, what is b?

A: Solving the given integral by substitution.

Q: Show that the equation is an identity.

A: x3+8x+2=x2-2x+4LHS=x3+8x+2=x3+23x+2

Q: 2. By hand, sketch the following against independent variable t: a) x₁(t) = Re(2e(-1+j2m)t) b) x₂(t)…

A:

Q: Find the GCD OF 4xy°z', 8x²y"z³ and 24x'y°z" ? 10

A:

Q: O For y = Asin (x- C)] + D Identify with graph A. B, C and D for the sin function y = -2sin (;x -) +…

A:

Q: (b) Find the points that touch the x axis of curve v = u? + pu + (n + 1). Where n=666. Also find the…

A: given the curve in u,v axis is as, v=u2+pu+n+1    where n=666

Q: 3) Find y" if y= 9 sin x.

A:

Q: Evaluate. 9- xp- dx%3D Evaluate. dx | dx = Evaluate. dx dx =

A: As per guideline we have to solve 1st 3 parts

Q: 3.) Given y=5* (2, 1)? which of the following shows the equation of the line tangent to y at the…

A: To find the equation of the tangent line to the curve   at the point .

Q: 2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y- 1) - In 2 =…

A:

Q: 1. Draw sketch graphs of the functions: b) y = (²) a) xy = -12 c) 2x-y=4 d)/y=x²-1 e) y = +4 = 2* -…

A: Note:- These are multiple questions with having sub parts. According to our company law we can do…

Q: 5) Sketch the graph of each function a) y=2" +1 b) y=3*1

A:

Q: The S- 3 dx is 5 sin 6x

A:

Q: y=2(21,2-1 + arctan x) 2 2 x-1

A: Please see the whiteboard.

Q: (6) Find дл ду : ye+sin(2)=423 (8 points)

A: Explanation is given below:Explanation:

Q: Find the distance between x = 10 -3 and y = ㅗ -5

A:

Q: _3. lim (17x – 4) х--18 А. -140 В. 310 С. -310 D. DNE

A:

Q: Determine the period of y = 2sec(πx-1)+3

A:

Q: i) P(5, 25) belong to y = x, what will the point P be transformed to after the equation transforms…

A: Real valued function

Q: 8c. Graph the line y = x +3 for -8 < x < 6 and then use geometry to calculate + 3) dr.

A: Answer is 35. Solution is given below....

Q: Find the equations of the tangent lines to the circle (x + 2)² + (y + 2)² = 25 at the two points…

A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Q: Graph the sinusoidal function using key points. 41) y = 1 + cos x 2- 1 -2n TC -1- -27 42) y = 4 sin…

A: Let's find.

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: Graph: y=sin(2x)+1

A: y=sin2x+1

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.