2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € R¹ and A> 0. Define Prove that αξ,λ u૬,A(T) := := 1 |x - ε|n-20 u (ε + № ²(x=0)). - 5/1²). is harmonic in its domain.

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Q: 2. Show that by using MEAN VALUE THEOREM . u-v < tan-1 v - tanu < if 1+v2 u-v 1+p2 0< u<v and ded…

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Q: Find the intervals on which the function is continuous. x +5 17) y =2-7x + 10

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: In approximating one real root of f (x) = on (1, 3), which endpoint of the interval is constantly…

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Q: 6. Find the intervals on [0,2r)where f(0) = sin²(0) is concave upward/ concave downw %3D

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Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

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Q: 77. Find - Ans. (sin t – cos t + e-t) (8+ 1)(82 + 1) |

A: Topic:- inverse Laplace transform

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Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: If f" CQ) = xa (x+)S (x-!) And all inflection points.

A: I have appended the concept used in the solution part

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A: NOTE: Refresh your page if you can't see any equations. . if the function h(x) is continuous at x=2…