√π T(m)T(n + 1) = ₂ = ₁ 1(2 Г(n)Г 2 22n-1 -T(2n), n > 0
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Prove that
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- (b) ka³ dx, where k, a>0 are constants. -2a (c) √ √√-x² + 4ax - 3a², where a > 0 is a constant. 1Solve (√x+x)=√y+y dx Select one: O a. y = (c(1+√x) + 1)² O b. y = (c(1+√x) − 1)² O c. y = (-c(1+√x) + 1)² O d. y = (-c(1+√√x) + 1)¹/² O e. y = (c(1-√x)-1)²√√√x + 1 -dx=y2 + 4y+4in(y-1) + C. express the final answer in terms of x. √x-1 Using Rationalizing Substitution 0+2√x+2ln(√x-1) + C Ox+2√√x+ln(√x-1)² +C x²+4√x+4n(√x-1) + C ©√x (√x + 4) + In (√x - 1)² +C
- d Find 3 + x(x - 1)). dx + 2х-1 +1 - 1 x2 -6 -+2х-1Solve(x√ √x² + y² + y)dx + (y√x² + y² + x)dy = 0 by Exact Method1 dx. x2-2x+8 Find I = Choose the factorization of the denominator from the following: Question 1) a. (z-1-iV7)(z+1+ iv7) b. (z-1-iv7)(z-1+ iv7) c. (z+1-iv7)(z-1+iV7) d. (z +1-iV7)(z +1+ iv7) e. (z - 1-iv8.5)(z + 1 + iVB.5) f. (z-1-iV8.5)(z - 1+ iV8.5) g. (z +1- iv8.5) (z -1+ iV8.5) h. (z+1-iv8.5)(z+14iV8.5) Question 2) Choose / from the following: a. 1.1417 b. 1.1874 c. 1.2349 d. 1.2843 e. 1.3357 f. 1.3891 g. 1.4447 h. 1.5024