HiWi Put a -af T ±aN #N If rit) =É é costi + e sint j +2 K

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: Let csct = V5,t e QII Find sin(2t) 4 O 2 V5 V5 25

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Q: Eva lua te the integral (1+z)e² Sinz dz, where C: |z|=1, by any two me thods and compare the…

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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: Show that coshr + sinh r = e" and cosh r - sinhr = e. Hence, deduce M MOUTMOUT cosh? a – sinh? r 1.…

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Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Q3 Evaluate the integral fei sin e dz, where Cis a circle |z| = 1.

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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: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

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: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…

A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…

Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: Supply the missing integrand and the limits of integration n/2 2sin e r cos?e dr de = | _de 2sin e…

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Q: e+e¯ (a) Find all the solutions of cosh z 4 (Hint: cosh z 2

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: 1. ò F 2 dt dt Ve' + 9

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

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: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

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Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

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Q: S sin y cos('/2) dy

A: ∫sinycosy2dy

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: The approximation of I = , tanx dx using composite Simpson's rule with n-5 is: None of the choices O…

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: Show that the function e cosy ti Siny) is an andlytic Runction 2 W= Sin Z Q2. Determine whe ther…

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Q: Evaluate the double integral : 4 3, 3x Si Si +14) dy dæ Answer:

A: Using integration formula we can solve this double integral

Q: Let y = cosh(ina²) then find y'. sinh (2n Ina) a. O b. O c. - sính(ina"). 2 O d. – sénh(2a. Ina²) O…

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Q: The approximation of I = tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 0.6236…

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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: Under what conditions for the contants a,b, k,e =) is (aa+by) da + (ka + ly) dy = 0 exact? Solve the…

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Q: dr Let A be the area of a circle with radius r. If dt dA when r = 3. dt 5, find

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Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

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Q: Let y = cosh(ina²) then find y'. Oa. sinh (2a.tra) -1 Ob. O b. O c. - sính(Inz²). 2 O d. - sónh(2a.…

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Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: The approximation of I = tanx dx using composite Simpson's rule with n=5 is: None of the choices…

A:

Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: dr Let A be the area of a circle with radius r. If dt dA when r = 3. dt = 3, find

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Q: The approximation of I = S, tanx dx using composite Simpson's rule with n=5 is: O 0.6158 O 0.6236…

A: First option is correct

Q: Use the trigonometric substitution r 2 sin 0 to compute the integral -2 VA – r² dx

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Q: What is the area inside the cardioid r= 2(1+ cos(4)), outside the circle r = cos(4)? 23л 11T 217 a)…

A: According to the given information, it is required to find the area inside the cardioid.

Q: The substitution 2=tan 2 transformed the integral dx Stadz, expression 5sin(x) – 12cos(x) + 13 into…

A: Consider the given integral ∫dx5sinx-12cosx+13 Take the substitution z=tanx2 to transform the given…

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

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Q: The approximation of I = tanx dx using composite Simpson's rule with n-5 is: O 0.6158 0.6165 None of…

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Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: Verify the rule by differentiating ∫ du/(a2 + u2) = (1/a) arctan (u/a) + C . Let a > 0.

A: Consider the given integral identity. ∫dua2+u2=1aarctanua+C Differentiate the LHS of the equation…

Q: Evaluate F· dr C where F(х, у) %3D хуі + уј C:r(t) = 4 costi+ 4 sin t and 0 <t<.

A: Given that , Fx,y=xy , yrt=4cost , 4sint and 0≤t≤π2 Evaluate ∫CF.dr=?

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: dy If y-3z sinh p z cosh y is exact, then n

A: