4. The teardrop x = 2a cos t – a sin 2t, y = b sin t, 0 < t < 27 find area y 2a

Q: 27. Inside the circle r = 3a cos 0 and outside the cardioidr = a(1+cos 60), %3D %3D a > 0

A: Find the area of the region inside the circle and outside the cardioid, where the equation of circle…

Q: Eliminate the parameter t from the following. x = sin t − 5, y = cos t − 4

A: Eliminate the parameter and simplify it.

Q: π/4 1 π/4 sin TX cos 2y sin 4z dy dx dz = 0 0 0 (Type an exact answer, using n as needed.)

A: Solution

Q: 4. The area which is inside the circle r = 8 cos e and outside the circle r = 2 cos 8.

A: Introduction: In polar coordinate, the equation of a circle centered at the origin with radius a…

Q: Eliminate the parameter t from the following. x = cos t − 2, y = sin t + 5

A:

Q: )Here are the graphs of the equations r=1+cos 0 | and r=3 cos 0. Calculate the area of the region…

A:

Q: Question 10 Using the method of Variation of Parameters, the particular solution Y, for the NHLDE…

A:

Q: 1. Given the DE as x(1 – siny)dy = (cosx – cosy – y)dx a) Prove if the given DE is exact or…

A: Given differential equation: x( 1- siny) dy=( cos x-cosy-y) dx

Q: 3 7 cos z Evaluate the definite integral: dæ sin x 6.

A: Evaluate the Definite Integral : ∫π6π37cosxsinxdx

Q: M3.2 Trigonometric Groups 3. S sin³x cos xdx 4. S Vtan x sec*x dx

A:

Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Determine the value of C in on the antiderivative of F(x)= sin (x)cos³(x) for x = 0.701 and y = 1.5.…

A:

Q: 4 .Using n=8 approximate the value of cos(1+Vx )dx using 0. (a) the Midpoint Rule, (b) the Trapezoid…

A: Formula used: Midpoint rule- The interval [a,b] into n subintervals of equal width,…

Q: 10. 3 J√cos z sin ³ zdz COS

A:

Q: 1. If H(y) = cos y – sin y, Find H (0), H (),H (1T), and also show that %3D + x) = H (T – x) = -H…

A: Given that H(y)=cosy-siny find H(0), Hπ2, Hπ Show that  Hπ2+x=Hπ-x=-H-x

Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

A:

Q: 7. d. cos 0 cos 20 + sin 0 sin 20 = V3 over 0, 2t)

A: We know the sum identities: sin(a+b) = sina.cosb + cosa.sinb sin(a-b) = sina.cosb – cosa.sinb…

Q: 2.4 sin x2 x2 +4 Find the approximate value of the integral dx by using one of the Closed Newton…

A: The given integral is ∫22.4sin x2x2+4dx We will use the trapezoidal rule.…

Q: 2. The deltoid x = 2 cos t + cos 2t, find area y = 2 sin t – sin 2t, 0 <t< 27 y 3

A:

Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

A:

Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

A:

Q: 9. Using n= 8 approximate the value of cos(1+Vx )dx using (a) the Midpoint Rule, (b) the Trapezoid…

A:

Q: The "equation cos x "y sin x is A Iny In (cos x) + k B Iny = In (sin x) + * c. Iny=-In(sin x) + k…

A:

Q: 4 Using n = 8 approximate the value of cos (1+ ya) dx using Using Trapezoid rule, and Display the…

A:

Q: 11. Find if y= cos(x) A. 2x sin(x) B. -x sin(r) 12. Differentiate: y=x cscx A. y' = cscx(1+x cot x)…

A: we have to differentiate the given equation . y=ex3

Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

A:

Q: 8) Determine the smallest positive roet of the equation - 0.0i t sin (0.573t) -e

A: To determine the smallest root of the given of the function we will use Newton-Rapson method with…

Q: 1 cos 3x dr b) VAr + 7 (In z)3 dr xe²? dx d) ſ e™ sin(e") dx e) f) sin x tan x dx (Hint: tan x = cos…

A:

Q: 1. The limaçon x = 2 cos t – cos 2t, y = 2 sin t, 0 <t < 2m find area y

A:

Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

A:

Q: Eliminate the parameter t from the following. x = sin t − 3, y = cos t − 2

A: Eliminate t by squarring

Q: 2. Find the length of the asteroid x = cos't and y=sin't , 0<t<2n. x = cos' t y = sin³ t

A:

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

A:

Q: 1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

A:

Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A:

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

A:

Q: 7. Prove: (a) sin iz = i sinh z. (b) | cos z|? = cos² x + sinh° y where, z = x + iy. COS

A:

Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

A:

Q: Find a possible formula of the form A sin t+k or A cos t+k for the periodic function with midline y…

A: The standard equation of any sinusoidal curve is given by  y=Asin(B(t-C))+D      or…

Q: 6) Find the linear approximation to h(y) = Sin(y + 1) at y =0 Use the linear approximation to…

A: h(x)=sin(y+1)  at  y=0 We know the that Linear Approximation of function f(x)=f(a)+f'(a)(x-a) for…

Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

A:

Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

A:

Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

A:

Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

Q: The function z =x^2√y is defined on the astroid x = cos^3θ, y = sin3θ where 0 ≤ θ < 2π. Use the…

A:

Q: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

Q: 9 3 12 6 cos (x) SSS dx dy dz =| 0 0 4y (Type an exact answer.)

A: