After applying change of coordinates to the following function, the new integrand should be VE ydydr O r sin? e O sin? 0 Or cos? e O cos? e

Q: S sin (Inw) dw

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Q: A. sine of e= d. cosecant of G= 36 39 b. cosine of e= e secont of e= c. tangent of e= f. cotangent…

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Q: et cos(t) Ry = e' sin(t) for 0 <t < 5 Find the length of the curve (Hint: You can simplify the…

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Q: Complete the steps by applying trig identities to show that the left hand side of the equation is…

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Q: After choosing the appropriate trigonometric substitution the integral| /4 dx, becomes cot2 tan tan?…

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Q: dy for each function below. dr 1. Determine (a) y = 3x COSI COS I %3D (b) у — sin r +1

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Q: Calculate dx - cos u for the following choices of u(x): (а) и(х) —D 9 — х? (b) и(х) — х-1 (c) и(х) —…

A: Given u=9-x2So, ddx(cosu)=-sinuddx(u)=-sin(9-x2)ddx(9-x2)=-sin(9-x2)(-2x)=2xsin(9-x2)Answer(a):…

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Q: Eliminate the parameter t in the following. x = cos 2t, y = sin t

A: Given that x = cos 2t; y = sin t To eliminate: the variable t Needed formulae: cos 2t = cos2t -…

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A: The objective is to find the solution of the partial differential equation ∂2ϕ∂r2+1r∂ϕ∂r+1r2∂2ϕ∂θ2=0…

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A: Given statement, EX2 is called the 2nd moment about origin.

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A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: Find the lengthof the curve r = a sin? (0/2), 0seST, a>0

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Q: Eliminate parameters A and B but not parameter C by differentiating x with respect to t. x=A cos…

A: x=AcosCt+B Differentiating wrt t, we get  x'=-ACsinCt+B Again differentiating, we get…

Q: dy of the following functi de A5) Find (a) y = sec(5r)[0.25 mark] (b)y = sin5x + cos6x [0.5 mark (c)…

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Q: Find the shaded area A4 in the given figure below

A: Here we have to find the area A4=?

Q: Perform the indicated operations in each exercise H(y)=cos y-sin y, find H(1/2π)

A: Given that:     H(y)=cosy-siny

Q: Which of the following is equivalent to -dx 1+ cosx – sinx after appropriate half-angle substitution…

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Q: The trigonometric substitution x= tan(t) 7 gives J 49 x2+1 dx= sec(t) Select one: O True O False

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Q: 2. Vy+1-2 dy

A: ∫vn dv = vn+1n+1+C

Q: Find Tand N for the circular motion r(t)=(cos 2t)i+(sin2t)j.

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Q: Find the measure of the given angle when given the value of one of its function. 1. Tan X = 7.22345…

A: We have to find the given angle measure in radians and degrees by using inverse trigonometric…

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Q: Which of the following is(are) true? (Choose all applicable answers.) O cosh z = e +e* 2. O coth a e…

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Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

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Q: 1. Evaluate the following trig functions a. sin d. cot b. csc- e. sec tan f. Cos C. 3 3

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Q: cos? e + cose +1 = 0 [0,2m]

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Q: Use D'Alembert's formula to solve the following (IVP): Utt in R x (0, 0) | u(x, 0) u(x,0) = sin (x)…

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Q: Calculate F(s), if given f(t) the following is bt e0 (6).f(t) = cos at - sinat -1

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Q: Find the lengthof the curve r =. a sin? (0/2), 0 s 0s 7, a > 0

A: Arc length of curve.

Q: Find dx or y' of the following functions and make any a. y = cot(Ve" ) tanh(e") b. Y =…

A: taking ln both side

Q: The modified Eulerimethad 2 use to solue X 20s y=l Sined y at x=0.l, h=0.02

A: Modified Euler method or Heun's method is another method to solve an initial value problem…

Q: Find the function r that satisfies the given condition r'(1) = (e!,c . r(0) = (5,5,5) Cos t, sec…

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Q: Find: y = arctan = 1 O a. none of these O b. 0 с. O d. 177 O e.

A: Given;  y=tan-1[(x+1)/(x-1)] at x=1.

Q: If y= sin?r+ tant, x= - In(- cost) – e inr, find the value of y' when 1= ". 2 2+ Vze VE 2-Vze 2

A: Given,y = sin2t + tantx = -ln(-cost) - esint

Q: Find Z, , Zy, Zy, Z, for the following equation: ху, Z= a x +cy° + c sin(xy) + d cos(y?), where…

A: We have given Z = a x3 + c y3 + c sin(xy) + d cos(y2)  Where a,b,c,d are constants)

Q: Find the lengthof the curve r= a sin? (0/2), 0sesT, a >0

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Q: Show that d?y dY + cot o- +a(@ + 1)Y = 0, 0 < 6 < T, do is transformed into Legendre's equation by…

A: Given:

Q: Assume a i gle in standard position whose terminal ang A side contains the point (5,-5) s to glpas…

A: The angle is in the 4th quadrant . Now find the length of the hypotenuse using the Pythagorean…

Q: If sint = - - and t is in the 3rd quadrant, then tan t %3D V45 45 O V45 V45 2 V53 O O O

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Q: Convert to rectangular coordinates. x = 1+ sin t, y = 1 + cos t for t in 0, 27

A: The solution are next step..

Q: Evaluate the following integral: ∫(cos⁡?)^5 dx    Pie/2 uppper  0 lower Where: sin(pie/2)=cos(0)=1,…

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Q: The integral B D a us can be transformed to which of the following using trigonometric substitution?…

A: Topic = Integration

Q: Differentiate. f(e) = e cos(e) sin(e) f'(e) = Nood Holn? Rend It

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Q: Find the equation of a sine wave in the form y = a sin(x + c) +d that is obtained by shifting the…

A: The given function is: y=sin(x)

Q: 1. SSin³ 3x Cos² 3x dx 2. JSin* 2пу Сos$ 2пy dy 3. JSin8 3пx Сos83пх dx 4. STan“ x dx

A: 1) Given:        ∫sin53x cos23x dx Using powers of sine and cosine :      substitute…

Q: Find L cosat by wing the methal

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Q: elt is evaluated by using what formula? O et = cos(x) + sin(x)i O et = lim (1+ )" n %3D n→0 п et =…

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Q: Find dy/dr for the following function y = cot-1 (x + sin? (5*))

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