az a2z az a2z at ax2 23. If z = sim(x+ sint), show that дх дх дt

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: (iii) 1 dø -sin²Ø Hint: may start with de (T(1/4)} /2 Vcose to obtain the result

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Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…

A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t  and z=1t To express dwdt in terms of t

Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

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Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

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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

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A: This is a problem of Laplace Transformation.

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

Q: O Find the equatisns if ou know The rootsa Dy=Ge -4X +Cze %3D 2X LG cos 3X t (z Sin3X %3D -3X

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Q: ze : use the Implicit Differentition to find ax 'ay 1) 3yz2 - e4* cos 4z - 3y2 = 4

A: 3yz2-e4xcos4z-3y2=4

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Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

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Q: Derivative rules Compute the following derivative.

A: To compute the derivative: ddt3t2i+tj-2t-1k.(costi+sin2tj-3tk)

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Consider 7(t) = (2t³ – 2, 3e“, – 2 sin(3t)). Find Don't include the +C. %3D

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Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

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A: We have to evaluate the complex integral ∫γfzdz, where the complex function fz=1z-2+sinh12z. First,…

Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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Q: 2πί -dz = 9. CoS z Iz=2 z3 + 9z :Select one True False

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Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: •2/3 Find dx. Hint: try either x = 4 sin 0 or u = 16 – x² as a substitution. 16–x²

A: Topic = Integration

Q: de B: Evaluate the 2m a-cos20 when z = et and Iz| = 1. %3D

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: T/2 TT/6 sin x 2 1.)Prove that

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Solve the following 1 do +- PDE: dr'r dr',2 20? BCs: v, dr at r=a v, =U„ cos 0 at r= 00 1 дф Ve = =…

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

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: Q3/ Determine: (a) sin(t) .8(2t – 1) (b) (cos nt). 8(t- 1)dt 8(t –

A: As per our guidelines we supposed to solve the very first question if the multiple questions are…

Q: 4. SET A. Evaluate di/dt, correct to 4 significant figure, when t 0.1 and I 15t sin 3t. %3D

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Q: 3) z = sin(ej³) + sinh(5230°)

A: We have evaluate the given complex number z=sinej3+sinh5∠30°

Q: Evaluate 7(t) dt: 4 4t -k; a = 0 and b = 4 t2 +1 †(t) -î + 2e4t cos t ĵ- t2 + 5t +6

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Q: 0. If 180° < 0 < 270° and cos e = -, find sin 20. %3D 13 O- 16V105 169 O 16/105 169 O sV105 169 O -…

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Q: ди ди then x +y = u. 31. If u = Jy² - x2 sin-

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Q: 1. Evaluate 2dt a. V5-4t-2t² b. Sdr r2+r-2 3r*+3r³-5r²+r-1 ) sin ()du с. os

A: Explanation of the solution is given below..

Q: Given x(t) = Acos (120 + p) = A1 cos120t + A2 sin120t. Find A1, A2, A and o when x(0.1) = -0.995 mm…

A: There is a typing error in the question. We have solved the question after rectifying the error as…

Q: Fand ar a of functrons COSX n

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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: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: z = 3e*jS, y = 3z2 + sin(z) iS l5 al: Jis dx

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Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: Evaluate: Jx?cos(2x)dx A None of the above 2x2sin(2x) – 2xcos(2x) + sin(2x) B + C 2x²sin(2x) +…

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