each-of-exercises-63-66-gives-a-function-fx-y-z-and-a-positive-number-epsilon-in-each-exercise-sho-4

Question

Each of Exercises $63-66$ gives a function $f(x, y, z)$ and a positive number $\epsilon .$ In each exercise, show that there exists a $\delta>0$ such that for all $(x, y, z)$ ,
$$
\quad \sqrt{x^{2}+y^{2}+z^{2}}<\delta \Rightarrow|f(x, y, z)-f(0,0,0)|<\epsilon
$$
$$
f(x, y, z)=	an ^{2} x+	an ^{2} y+	an ^{2} z, \quad \epsilon=0.03
$$

Uma Kumari · Accepted Answer

it is given that a four x com Abiko mazie is equals toe the engine square eggs plus tangent square by plus tangents. Classy. Let their ties equals toe the engine to the bubble, minus 10.1, then ex Morley Smaller than data. Why mode is also smaller than data on Z mode is also smaller than data. We get a four x com Abiko matzzie minus I from zero comma, zero comma, zero more as equals. Toe the engine square eggs plus the engine square by blast. Ancients close e whole mode. It would be equals toe. The engines were expressed. Engines were by plus stands in square see, which is equal to 0.1 plus 0.1 plus 0.1 It would be equals to 0.3 which is equals to excellent Does the solution is absolutely is equals to 0.3 This is the final answer

Uma Kumari · Answer

it was given that f o X com Abiko Mazie is equal to X plus by policy. A phone a Square plus Vice Square plus the Square plus one let Delta&#x27;s equals to 0.5 then x more is smaller than data. Why mode is also smaller than Delta on Z. Mood is also smaller than Delta. We get a four x com Abiko matzzie minus fo zero comma, zero comma zero whole more is equals toe Express by policy Born X squared plus y square plus the square plus one. My new zero call more It would be equals toe X plus y plus Z, divided by X squared plus y squared plus the square plus one pull more, which is equals Toe X plus five plus zero or more. It would be equals two x more plus by more plus e mode, which is smaller than 0.5 plus 0.5 plus 0.5 which is equals to 0.15 which is equals to absolute does. The solution is absolutely is equals to 0.15 This is the final answer

Uma Kumari · Answer

it has given that a four x com Abika mercy is equals. Toe X squared plus y squared, plus the square leg Delta is equals toe under 0.0 and five. So under rude eggs where plus y squared plus C square the smaller than data it gives us F o x com Abiko Matzzie minus fo zero comma zero comma zero whole mode is equals toe X square, plus by square, plus the square. My new zero hold more it would be equals two x squared plus y squared plus C square. Holy more We get on the road a square plus y squared, plus the square who&#x27;s square a smaller than under Route 0.0 Gunfight whole square. It would be equals to 0.15 which is equals to absolute does. The solution is absolute is equals to 0.15 This is the final answer

Uma Kumari · Answer

it is given that f o x com Abiko Matzzie, This equals two x into my embassy lead. Delta is equals to zero point toe. Then X motor, smaller than Delta by mode, is also smaller than data on Z mode is also smaller than data. We get a four x com Abiko matzzie minus a 40 comma. Zero comma zero whole mode is equal to a four x comma by commas e minus zero. Hold more. It would be equals toe extent to buy into the mode be good x mode and to bi mode and to see more, which is smaller than zero point to hold. But simplifying it we get 0.8 which is equals to absolutely does. The solution is absolutely as equals to 0.8 This is the final answer.

Uma Kumari · Answer

it is given that a forfeit Skomal is equals. Toe explains why divided by two plus co sign it let mhm their ties equals to 0.1 then goes in. It is greater than equals two minus one and smaller than equals to one, which gives us two plus co sign. Eggs is greater than equals to one and smaller than equals 23 we get one upon three is smaller than equals to one upon to place cause Hynix Elevator smaller than equals toe one. It gives us explosive by more. Divided by three, they&#x27;re smaller than equals toe explosive. I divided by two place for cynics. Whole mode, which is smaller than equals toe explosive by mood, which is also smaller than equals traits. More plus fine work, then make smaller, smaller than Delta on by Mode is also smaller than that and gives us a full fix coma by minus fo zero comma zero whole more is equals. Toe explains why divided by bless goes Heinicke minus zero hole more, which is equals to express by divided by two plus co cynics. Whole morgue well, which is smaller than equals toe, takes more plus five more. It would also be smaller than 0.1 plus 0.1 which is equals True zero going 02 which is equals to excellent. There&#x27;s the solution is absolutely is equals. Toe 0.2

Uma Kumari · Answer

in this problem, we are given fo X y is equals toe under rude X Square, plus Why square and a positive riel number Exile in is equals to 0.1 and we have to show that Delta is greater than zero for all such that X comma, vile and under rude X Square plus Vice Square is less than data and moored off fo x Y minus fo 00 is less than a silent now lead days. It was 20 point what we take under root X squared plus y square less than that now, which gives us under X squared plus y square less than 0.1. We can also write this as X squared plus y square less than 0.1 by taking square both sides. So we have a model F o X y, minus fo 00 more is equals toe model X squared. That&#x27;s why square minus zero less than 0.1 which gives us mortal echoplex life minus fo 00 less than 0.0, while equally toe of silence. Therefore, the solution is model f of X y, minus fo 00 less than 0.1 is it was toe Obziler

Problem

Show that $f(x, y, z)=x+y-z$ is continuous at eve…

Problem 66 Hard Difficulty

Answer

$\in=0.03$

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$\in=0.03$

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George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. GiordanoThomas Calculus

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George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano

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