If sin x = siny = a and cosx = cosy = b, then cos(x-y) is Select one: O a. z2 + a² O b. 2b + 2a O C. 62 – a?

Q: Given z = (e-2) (siny), find dr -2x O-2 e 2² (cos y) O-2 e 2 (sin y) O-2 e 2 (sin y) +e-2 (cos y)…

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Q: Given: [ Scos(cos2x) sin2x dx Find: du O 2cos2x dx O -2sin2x dx -2cos2x dx O 2sin2x dx O O

A: ∫coscos2xsin2xdxLet u=cos2x.So,     du=-2 sin(2x) dx

Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0). Leave your answer correct to two decimal…

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Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: Practice by Evaluating 1 VI-x² cos(a² + y³)dydx 0.

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Q: If 0 < 0< and z= (sin 0+i(1- cos 0)) find in its simplest form arg z.

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Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

Q: If Z = cos () +i sin then Z-Z+1=. .

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Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.…

Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: TT/2 S,"/e cos?x.sint x dx in tegralinin bulunvz sonucunu

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Q: Given that sĩn = %3D 2 |cos 플 호 and COS %3D sin = cos 4 = show without Ee using a calculator that…

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Q: The cos'ydy is equal to 3 A. siny + sin?y +sin³y - sin'y+ C sin'y + C 3 1 B. siny – sin³y + siny -;…

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Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: Show that 0 π/2 st sin? xdx TT/2 [ 0 cos? rdr 2

A: A detailed solution is given below.

Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

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Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

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Q: 4. Evaluate the following and give the exact value: - Tt/4 r2 cos 0 crsin 0 r2 cos 0 dz dr d0 0,

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Q: Given 5y + cos(3y) = x³ Implicitly find dx Select one: 3x Sy²+sin 3y a. 3x O b. 5y²-sin 3y C.…

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Q: If A=2(1-cos 0)â, – pyâ, (1– cos ¢)â, – ppâ, +zcos² þ⸠, what is 4 8. V•A ?

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Q: If f(1, y) = e“ sin 7y, then fay is given by: o - 28 et sin 7y O - 28 e“ cos 7y O 28 e" sin 7y O 28…

A: Given that: f(x,y)=e4x.sin7y

Q: 6 3 oy sin (a? + 3²) dædy Find

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Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

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Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find fx(8,9,0). Leave your answer correct to two decimal…

A: Solution

Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

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Q: What are the values of and cz so that y(x) = cq sin(x) + c,cos(x) will satisfy the conditions y(0)…

A: Given y (x) = c1 cos(x) + c2 sin(x)and y(0) = 1,   y'(π) = 1

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: Which of the following is equal to s v² cos (v³)dv ? A sin 1 8 jsin 1 O Option 1 Option 2 D. sin C.…

A: The solution is Option B 13sin(1)

Q: 2 (cos Fe tisin) - fsih 똥) Q) put Vz (cos 3+P sin I) 6. in expoitial hor m

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Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: If P = 2 sin(10t + x − π/4)ay and Qs = ejx (ax − az)sin πy, determine the phasor form of P and the…

A: Given- If P = 2sin10t + x - π4ay and Qs = ejxax - azsinπy To find- Determine the phasor form of P…

Q: The cos'ydy is equal to 3 1 A. siny + sin³y + sin³y -; sin'y + C 5 3 B. siny – sin³y +sinsy -sin?y +…

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Q: f(8,t) = cos os(0e*) + cos( + e*) = COS + cos (s+

A: Find partial derivative.

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

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Q: Which is equivalent to ſ sin y cos(/2) dy? C/2) dy? a.) S [sin("/2) – sin ("/2)] • dy b.) S sin("/2)…

A: The given integral is: I=∫sinycosy2dy As according to trigonometric formula:…

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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

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Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: Using an appropriate substitution, f sinº (x)cos'(x)dx is equal to: cosl +C 11 cos 11 O Ths opton O…

A: We will find the integral by substitution as following-

Q: A certain substitution gives S sin*x)cos"(x)dx = S (u²-u*)du .what is n?

A: For substitution- Balancing the above equation, we can solve it as follows-

Q: 1 La So cos " dy dæ COS evaluate

A: We are given the Integral: ∫π2π∫0x21xcosyxdy dx=∫π2π1xsinyx×1x0x2 dx=∫π2π1x2sin xdx It cannot be…

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

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