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

A: here we will find AB,

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: дz əs дz at || 11 z = e cos(8), r = st, 8 8 = √ S6 + 56

A: Solution is done in step 2,3

Q: EVALUATE USING HALF-ANGLE SUBSTITUTION dx 5 + 4 sin a A. aretan (Stan (3=) + 4 arctan +C 3 В. 2 5…

A: This question is based on indefinite integral.

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: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: If f(z, y, z) = sin(z) +ay2-23 then the value of a that makes div(Vf) = -sin(z) - 6z is Answer

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Q: cosh? z + sinh2z=1 true False O оо

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Q: Q: If cosece - sin e = t and sece - cos e = m, prove that l'm? (12 + m2 +3) =1 1. %3D

A: Given that cosecθ−sinθ=lsecθ−cosθ=m

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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

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Q: 6. If f(x, y, z) = r³y³ sin (z²)+z³ cos (r³), find an expression for fryz and evaluate it at the…

A: x, y and z are the variables of function f Differentiating partially the function f with respect a…

Q: π/3 So, f²ef/³ t In u tans ds du dt

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Q: 2. It Z = e tanly) , wnere x = S"+ t and y=St, find 22 when S=1 and t =0 2t

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Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is ∫-π4π4sec2xdx

Q: B) Find (블)x,()'(일), Prthe Pte 2- w= x?+y-2 +sin z 3. w:x+y+2", ysinz+ z sin so

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

Q: dz dz Find Ju when u = In 2, v=5. if z = 20 cot 'x, and x= e" + sin v. and dz (Simplify your…

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Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: if z sin とこ3r'+25 , Y=4イ-ス3 Z = 2r-35* W= Z Sin %3D * find aw,w ar me' me as

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

A: Given,Z=Sinx+sintto prove∂z∂x·∂2z∂x∂t=∂z∂t·∂2z∂x2

Q: 4. Find Rable With respect ho X and X is also iable nith respect b . a ssuming fhat Y is diffrent…

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Q: 6. SS dV に lies b/w ミ 25 %3D and x? f y? + z? Ź 36 in the firót oct ant ...

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Q: ind r. f'(t) = sec(t)(sec(t) + tan(t)), = -3 f(t) Need Heln? Read It Watch It

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Q: D. Use the Wronskian to detcrminc whether or not the vcctors arc independent or not (the answer for…

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

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Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: If fiß->(0,4) and I 9s an interval on which fhas both values, then t has Oi discontinutty 9n I,

A: Consider the given information. f:R→0,1 As given I is an interval on which f has both values. If f…

Q: which of the foliowing is a vaiid equ be us ed to Soiue for 2 ak di altan 40=x 60 60 bl Sin 4O= 40…

A: Given : A right triangle

Q: R² and r are defined by SR E(*; – T)(yi – ỹ) Say R? SST' r = VE(x; – #)² L(yi – g)² (1) Show R² =…

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

Q: R Given: RT = QT, AT = ST A s, Prove: AQSTARAT

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Q: If Y(t) = X(t + a) – X(t – a), prove that R, R. (T- 2a). Hence prove that Sy„(@) = 4 sin“ ao S„(@) =…

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Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: Ifcesese - sin e = t and sece - cos e = m. prove that 1'm? (12+ m? +3) =1

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Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

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Q: Given: 41 24 Ris the midpoint of PT Prove: 2Q L 1/2 X P

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Q: Q:9 Evaluate cot(72)\dz 3 [z e? + by Cauchy's residue theorem.

A: We have to solve the given integral by Cauchy residue theorem

Q: Solue the differeulial equalion dy +9-é^ Cosre zo yo) =0. 2. by csing milne's methad with h = 0.1.

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Q: c. Use De Moivre's theorem to find the following: 4 i. [1+ v3i]*

A: Dear learner, As per our guidelines, we can provide the solution for first one only. Kindly post…

Q: 4. If f(r) = sin(r), can you determine D(2021) f(a)? Explain.

A: 4)

Q: Evaluate F di where F = (4z, 0, - z), and C is given by 7(t) = (t, sin(t), cos(t)), 0 st<R

A: Use parametric to solve

Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

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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: dy +. (x>0) tind the Soiution of the difperential equation, expressing 4explicitly as general 4…

A: First we comparing the given differential equation with dy/dx+Py=Q .and then find I.F. and then…

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: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

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Q: Step by step explanation how to solve this problem.

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Q: We have r(t) = (2e-t, sin-'t, In(1 –t)) , %3D Find 1- The domain 2- ar , an, T, N and t at t=1

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

A: Ring Theory.