1 Operating R2→R2 -2R1 , R3→R3-3R1 14. = 2 Expanding along C1 we get ∆ =a3 2 15. 1 simplifying we get, k= 1/2 1 2 16. Differentiating w.r.t x 1 Again differentiating w.r.t x we get 1 1 1 2x-2y-2 -4y=0 17. 1 1 Since the tangent is parallel to Y-axis, y-2 = 0 Substituting the value of y, and getting the points (3,2) and (-1,2) 1 1 Put sinx = t ; cosxdx= dt 18. 1 I = = 1 =[log(1+t)-log(2+t)] =log
1 14. Operating R2→R2 -2R1 , R3→R3-3R1 = Expanding along C1 we get ∆ =a3 2 2 15. simplifying we get, k= 1/2 1 1 2 16. Differentiating w.r.t x Again differentiating w.r.t x we get 1 1 1 1 17. 2x-2y-2 -4y=0 Since the tangent is parallel to Y-axis, y-2 = 0 Substituting the value of y, and getting the points (3,2) and (-1,2) 1 1 1 1 18. Put sinx = t ; cosxdx= dt I = = =[log(1+t)-log(2+t)] =log 1 1
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