(S U T)' = S' UT' S'UT'

Q: 1. AB and AC are tangent to OP. Find AB. 4 3y +4 B 1ly

A: here we will find AB,

Q: ind F(t)dt (don't include the +C) + C

A:

Q: S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

A: Given that, f(x, y)=sen2r2-θ2+lnrθ+θfor r=x2+y2and θ=arctanyx

Q: Given z = 2t -41 and y=4 sin t %3D dy (i) da dy (ii) da?

A:

Q: 28) To evaluate S dt we could use the substitution a) t = sin(u) b) t = tan(u) c) t = sec(u) d) t =…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: find the geeral aluten for d'y dy du Ay= eax (1+u*) du2

A:

Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

Q: Evaluate S dz over C, where C: |2+1| =1 O i pi

A:

Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

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Q: If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

A:

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”.

Q: 3. y = 1+Vx eğrisi, y = 3 – x doğrusu ve eksenler arasında kalan bölgenin koordinat düzleminin 1.…

A: Given the curve y=1+x, and the line y=3-x. Find the area between the curve, line  and bounded by the…

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

A:

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

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Q: Fain the par hicul ar foluhion 4 DE . 9xy dy ; uh en x= 2,y=1 4xy° dy = 2y (1+ y?) dx ; when x- 2…

A: In this question we will use basic of calculus i.e contact of solution of differential equation. We…

Q: find dy ny the Chaenin Rult yz tan u and UzJxz+5

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Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: dw when r= 3 and s = - ar 3 if w = (x+ y + z)“, x=r-s, y= cos (r + s), z= sin (r + s). Find

A:

Q: Find the general antiderivative. If the substitution method is used, state first u, du and [lu)du.…

A:

Q: et u = e Sin P= sin sc Lind su using chain Rule

A:

Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: (r(1/4)|? 4u/27 dv Prove that

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Q: L[cosh(@ot) u(t)], C[sinh(@et) u(t)] and L[cos (@t) u(t)

A:

Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: 2 = e" cos u = e – r, v= re".

A:

Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

A:

Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

Q: 3. What we want to do next is write (x + jy)as Reie where R= J(x? + y? ) and tan-(e) = (2)

A:

Q: After substitution is performed, what is equivalent to u14 du 3 0 9 Su u¹4 du ,14 1. 3u¹4 du 0 2 u¹4…

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Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: et sin t? blas Y - et cos t? lio -n/2 <t < 0

A:

Q: dy IS let y = (cos r)m " then de sin z

A:

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: If r(t) = (V10 – t, In(t – 1), sin(2t)) , then the domain of r is

A:

Q: 27. y" + 9y = r(t), r(t) = 8 sin t %3D

A:

Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

A:

Q: 3. If y = w sin w, then what is dy/dw??

A: y=wsinwTo find d2ydw2

Q: 6. Write.a.Ct).in. the farm..aaT.T+ a. N. a..r(t).=(tcost). .+ (tsint.) j.+t ..to.

A:

Q: Ex 15: Prove that : d du a) tanh u = sech² u dx dx

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Q: Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

A:

Q: dy x fanx

A:

Q: If u=lx+my and v=mx-ly,show that 1? + m? ди ди 1 + m?

A: Given  u = lx + my v = mx - ly

Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

A:

Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

Q: dy _ 2y 4. If tan(ry) + 5= ry then show that dr?

A: We have to do differentiate with respect to x.

Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.