(2) Separation of variable c. xcos?ydx + tanydy = 0

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

A:

Q: Find the area between the inner and outer ovals of the curve r2 = 16(2 – cos 0)

A: Given,

Q: a.) Evaleiate. (6tanx dx

A:

Q: xy sin y dAR: - 3sXs3, 0sysn SSwsiny dA= xy sin y dA =

A: Use double integration to evaluate it

Q: Determine the integrating factor of the Bernoulli's equation given pelow: dy -y cot2x = y' csc2x dx…

A: ................(1) substitute take derivative .................put it back in equation 1

Q: Fiud ť amalytic Ť Ref = (t+y) · cos(2=y").

A: The objective here is to find f analytic. Ref=x+ycosx2−y2

Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

A:

Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: The change in heat radiated by a body, detected by a pyrometer (non-contact temperature sensor), is…

A:

Q: Find the circumference of the curves x=e^-2θ (sinθ+cosθ), y=e^-2θ (sinθ-cosθ) over the interval 0 ≤…

A: To find: The circumference of the given curves. Given information: Concept used: If a functions are…

Q: Find the area between the inner and outer ovals of the curve r2 16(2 – cos 0)

A: To find the area between the inner and outer ovals of the curve

Q: 2y у'+ — х?у? sin x %3D

A:

Q: ula 0ニ こ0 2

A: Find solution using variable separation.

Q: xcos²ydx + tanydy = 0

A:

Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

A:

Q: dy IN QUESTIONS 1-13, FIND dx' 11. y = x®tan³x 12. y = Vcot3x 15. y = cot"(4x + 9)

A: Find dydx for the following (11) y=x8tan3x (12) y=cot3x (15) y=cot74x+9

Q: Find the equation of the tangent line to r = sin3θ  at θ = π/6

A: The equation of the tangent line to a curve y = f(x) is: where m is the slope of the tangent line m…

Q: 26) y = tan((T/6)x) Period: TT. -217 -ㅠ TT 21T -2 -1 -1 -2 -ㅠ MCL @01 %24 ElN-

A:

Q: Sect sec't dt Tari'la)

A:

Q: cos(3t) sin(8t) dt

A: we use  2 cos A sin B = Sin(A+B)-sin(A-B) sin(-x)= sinx

Q: Find the area of the region that lies inside the curve r = 2+ cos 20, but outside the curve r = 2+…

A:

Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

Q: ∫cos(3t)sin(8t)dt

A:

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

A:

Q: Differentiate.   y  = Cos h -1(Sin h x)

A: Given inverse hyperbolic function - y = cosh-1sinhxUsing Chain rule, differentiating on both sides…

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: the regions enclosed by the given curves. y = 6 cos(5x), y = 6 sin(10x), x = 0, x = 1/10

A: Given: y = 6 cos(5x) y = 6 sin(10x) x = 0,  x = π10 To find: Area in between the two given curves.

Q: cos° (2t) 23. sin (2t) dt

A: Use the formula sin2x+cos2x =1.

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

A:

Q: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: 1. y = sin x at , 1)

A:

Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: Find y' and y". . sin3y=x²+tany+1

A:

Q: Inside the circle r =3 sin 0 and outside the cardioidr 1 + cos 0

A: The area that we have to calculate is the shaded area in the diagram above.

Q: 1 (s +1)(s² + 1) - cos t + sint) + cost – sin t) Option 1 Option 4

A:

Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh (15)+cosh (31)

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: find the arca of he shaded regon. Ue a calcularor apter xmng up tde integal. cos 20

A: Let r1=cos2θ and r2=2cosθ. We know that a polar coordinate is represented as r, θ, where r=x2+y2 and…

Q: S 4 cos (x) sin (x) dx = %3D

A:

Q: 3. Find if (a) y = 22" In (cot (7x)*) (b) y = sin? (Arcsin (T) +e-*)

A: Part(a) We have y=22xlncotπx2 We will use product rule and chain rule.  Product rule says:…

Q: 5 cos(a) sin (x) dx

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: What is the area within the curve r = cos 5θ?

A: For the solution follow the next step.

Q: Question 12 of 12 fe #0. dz and ye-8 sin 4z = 4z %3D dz dx dz dy II

A: The objective is to find the partial derivatives.

Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh'(15)+cosh (31)

A: according to the guidelines of bartleby I will do only first question please ask rest of the…

Q: 2 [arc cos ( Incs-2) fdz ( Incs-z>) ] dz

A:

Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution is given below