Show that cos λx 2² +1 -dλ TU že 2 x ≥ 0.

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: Use the 2 solutions Bernoulli's equation y' + -√√y=0 y x

A: The given differential equation y'+yx-y=0. We have to find the solution of the differential…

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

Q: Let z=x+ iy with x and y are real. What is the imaginary part of sin (x + iy)

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Q: A solution to the partial differential equation. 9. is dy?

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Q: If z = cos (r + cos y), show that az Fz ar ərðy dy dr

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Q: Find dy dx 3) y = cos = cos¹ 2 2x

A: We have to find the derivative of y

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Qlif y= fcus and u=x46x +5 U =X and - 2u -1, Sind dy dx

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Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: [(1+cos 3x) dx 3x)?dx + cos

A: Given: I=∫(1+cos(3x))32dx

Q: Show that cos A x e 2 *,x2 0. %3D

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Q: 1: Find dy if y³-4y² = x³ + 3x². dx 2: Find DPP 7 DERIVATIVE dy dx if sin y² - cos x² = cos y² + sin…

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Q: Find the next vector spacing and wrap A = 1(x +y) +j + zx) + k(2 +xy)

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Q: Find the expression for dy dx dy dx dy 2xcos(x²-y²) - 1 2ycos(x2-y2)+1 dx The answer cannot be found…

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Q: fx = 4y sin(x) and fy = 4y + 4 cos(x).

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Q: Vx2-1 dx

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Q: For | cos 3x cos 4x dx :

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Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: Let Then dy dx = y = tan-1 √4x² - 1)

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Q: Verify directly that the relation y = C3 e cos bx + c4e sin bx satisfies the equation [(D – a)² +…

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Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: xp sin 5x cos 3xt cos 5xsin 3x xp x²+ 2x + 5 EX Find:

A: