Given: lim e -e = 2e Use only E- d defini tion of a function limit to Prove: 2×+イ 2a +1 ニ2e dx Hint: use E-S proof technigue on the for mal depinition OF a derivative. Then use the given to bouma -e 2el
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- 2. (19) Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter 00 or 00, as appropriate.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.2.(11) Determine the following limits. Enter DNE If the limit does not exist.
- 15.2.18 #8 Evaluate the following limit. lim ln 3sqrtxy (x,y)→(27,e^9)Use the Two-Path test to show that the following limit does not exist. (Use y=x2) lim (x,y)→(0,0) (x2y)/(x2+y)2I have one follow up question: Check your hypothesis from part (d) above by now finding the derivitive g(x) using the limit definition.
- Given ????→1 (3? + 7) = 10 and Ɛ = .001, find delta function >, 0 (using the formal definition of a limit). Show all work.2. (17) Determine the following limits. Enter DE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter 00 or 00, as appropriate.Let f (x, y) = x3 + y3/xy2 . Set y = mx and show that the resultinglimit depends on m, and therefore the limit lim (x,y)→(0,0) f (x, y) doesnot exist.