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- If x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xyFor an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.1. Use the definition of the limit ( epsolon - delta ) to show thatlim of 1/z as z approaches -i2. Give the condition which ensure that |ez| < 1 where z in C.
- Compute the limit (x,y)→(0,0) of 8xy / 2x^2+ 4y^2 along the following paths. (a) Along the y-axis. (b) Along the line y=3x. (c) What can you conclude about the limit?Evaluate the limit limn→∞ ∑ n i=1 f(ci ) Δxi over the region bounded by the graphs of the equations.Prove that limit x goes to 2 x^(3)+3 = 11 (Using epsilon-delta proof)
