Evaluate: S ndy 2y+3 (y 1)(y 1) In G) ny² + y + 1| - arct arctan 0 Inly 1| ž(y 1)* nVi y arctan( ) c 3. O Inly 1 () + ny? + y + 1] arctan( ) y1) 3. + C
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A: As per the guidelines we can solve 1 problem only
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A: a). ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…
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Q: In z 25 If the triple integral So" Sõ So™² (xe¯y) dydx dz Find the upper limit value E.
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Q: 25 3. In r If the triple integral fo So So (xe") dydr dz Find the upper limit value E.
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Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – -dy y? (1,2) Moreover evaluate…
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Q: 4 Find the mul hiplicity of the foll owing faunchons 3 2. a-9xt 30 L -4yx at x= 3 and x=2 3. 2. ) f-…
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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – x dy. y? -dx + (1,2) Moreover…
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Q: 2 1 Evaluate the iterated integral S 18*y°dy dx. -2 0
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Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D
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Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these O…
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- Prove cosh 2 x - sinh 2 x =1Hpw to solve this without L'hopital's ruleSuppose U solves the heat equation on the real lineUt = 4Uxx, x ∈ Rwith initial valueU(x, 0) = (4, x ≤ 02, x > 0.(i) Use the Fourier-Poisson formula to give an explicit expression for the solutionU.(ii) Describe the qualitative behaviour of U in this case as t → ∞ and plot outthe solution at several instants of time to explain your answer. What is the limitof U as t → ∞?
- Find the work done in emptying the tank in example 4. If the tank water is pumped to a level 1.00 meters above the top of the tank and the water is initially 4.00 meters deep.limx→0 (1−cos(5x))/(1−cos(9x))Currently stuck on a divergent problem and would like some light on how to solve this. Much appreciated, thank you.