Evculucte the ntegre ree)dt where re =secttleH, tine TNt C 2

Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

Q: f(z) = dt olarak tanımlansın. f'(-1) Deriyatiye's Value ? %3D O a. 1 O b. O c.-1 O d.- e. 0

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Q: A particle moving along R(t) = r cos tî + r sin tj, r > 0, has an instantaneous speed that varies…

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Q: Find J, ()dx Chint:let Z=Jx)

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Q: The area A of a triangle with sides of lengths a and benclosing an angle of measure u isA = 1/2 ab…

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Q: (D² + 2D- 3)y = si %3D

A: Here we use auxlary equation to find complimentary  solution.

Q: 2 cos Ø sinotos"0 csc0 Reuorite the expresson as a single triganometrie function whose anqument is…

A: Given: The expression 2cosϕsinϕ+cos2ϕcscϕ, To simplify: The given expression in term of one…

Q: The acceleration of a particle moving back and forth on a lineis a = d2s/dt2 = π2 cos pt m/sec2 for…

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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: If r (t) = (sin(t), cos(t), 2), then ſr (t) dt = 0.

A: The vector function is given by rt = sin(t),cos(t),2 To evaluate : ∫0πrtdt

Q: angleO: Find a Tayler saries for Hhe Sunction fa)= In G) contered at a=I

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Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

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Q: O! Find tue indefinite integrel by q meleing tue febstelion d=4 Sin o. 2 *7 16-x"

A: To determine: by substituting x = 4sinθ

Q: r(t) = (tan(5t))i+t cos(t)j – Vtk

A: Given: rt=tan-15ti+tcostj-tk

Q: The work done W,to stretch a spring from its natural length to an extension of b meters Is 6. given…

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: 3. The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given…

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Q: Given that S" 4Væ dx = 152, what is fo*4Vt dt ? 3 )

A: As we know that;  the value of definite integral will not change if independent variables changes,…

Q: find dy/dx

A: According to Leibnitz  rule of differentiation:

Q: 2. In 00, AE is tangent to 00 at E, mZBCF =112 and mBE:mDE = 3:7. Find: (а) тBE (b) mZA E A В (c)…

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Q: 1. ò F 2 dt dt Ve' + 9

A: The integral function are 1. ∫etet+9dt   2.∫2t+4ttdt

Q: du Q. Show that du and dy for u = In Vx2 + y? %3D dy and v = tan

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Q: 1) Let c. 12i| =3 and I = e dz. then %3D I= 1o TTi? %3D

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Q: The area A of a triangle with sides of lengths a and benclosing an angle of measure u isA = 1/2 ab…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 2. In 00, AE is tangent to 00 at E, mZBCF = 112 and mBE: mDE = 3:7. Find: (а) тBЕ (b) mZA E A C (c)…

A: In circle with center at O, we have following diagram We have to find (C) m<DEB

Q: Using a suitable substitution, the integral T/4 9 (13+tan t)8 sec? t dt of

A: Given,          ∫0π4913+tant8sec2tdt

Q: 2. In 00, AE is tangent to OO at E, mZBCF =112 and mBE :mDE = 3:7. Find: (а) тBЕ (b) mZA E A В (c)…

A: Circle

Q: Is AB a tangent to OC? 29 C 10 A Your answer: nt o Yes, AB is a tangent. No, AB is not a tangent.…

A: We have to check

Q: Classify each of the following equations as to order and degree. dy + (ху — сos x)dx %3D 0 d²Q + R…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: d Jcose d cose 'cos(r sin 0)]= [e* Telcom sin(tsin 0)]. (i) Show that t. %3D dt

A: (b) (i) show that t·ddtet cosθ cost sinθ=ddθet cosθ sint sinθ consider left hand side  t·ddtet cosθ…

Q: If r (t) = (cos(t), sin(t), 2) , then fr (t) dt %3D

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Q: 10. Prove the following formulas : d cot u = – csc u. dx d CSC и 3 — csc и.cot и. dx 2 du а ) * dx…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: what is the Folution when i =0 and t= o ? di + Ri = Esin 2t %3D dt

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Q: az or and as dz az Using the given information, determine dt 3. at az = 2 ax az dx dy =1, ду (a) 4…

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Q: 10. Prove the following formulas: du cot u %3D-сsc и. 2. а ) a dx d dx du csc u = - csc u.cot u. b)…

A: (a) ddxcot u=dducos usin u·dudx=dducos u×sin u-cos u×ddusin usin2 u·dudx=-sin u×sin u-cos u×cos…

Q: sing Laplace trans form to Solve :- dt? dy +25 dt +24=5sint where yl0)=y (0) = c

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Q: dy 3. da + y = 2xy?e"

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Q: 25. z arctan r dr dr 26. Jo (z – 1)² 27. e sin z dr

A: A detailed solution is given below.

Q: tione in detai 0 Ose dapaie teamfaven to rolve d'y + d dy ty=tet d+2 %3D dt with ylo)= 1 = %3D

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: dt | 65. Use the substitution u = tanh t to evaluate cosh? 1+ sinh?t"

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Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

Q: fi at nd laplace: {e}

A: Use the formula for the Laplace Transform for the given function.

Q: u(x, t) = ear+bt %3D 1 u(x, t) = -/at %3D

A: The given functions are ux,t=eax+bt and ux,t=1te-x2/at.

Q: A particle travels along the helix C given by 7 (t) = cos ti + sin tj + 2tk and is subject to a…

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Q: Can i get help step by step please

A: Let q=q*sinq and v=q^2-1 Find u' and v'. (First derivatives of u and v with respect to q)

Q: DE -そ しet E =BDNAF. BA F. It CD 4o m and CB=30m, derermlne. a) 1he quadrilatiral CF EB area BG BD.…

A: Pythagoras theorem is applicable on right-angled triangles to find the missing values. The…

Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given: