Please be sure to answer the questionProvide details and share your research! 3,304 2 i think you dropped a sign somewhere, but i would go as follows x 2 y 2 = x 2 y 2 0 = x 2 y 2 ( (xy) (xy)) = x 2 xy xy y 2 but as I think Mark was pointing out, all the steps you took working from RHS to LHS are perfectly valid in \(\displaystyle Prove \lim_{(x,y) \to (0,0)}\frac{2xy^2}{x^2y^2} = 0\) There are probably many ways to do this, but my teacher does it a certain way and I would like to learn his way first (although I am also interested in other techniques–perhaps
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Prove (x+y)^2=x^2+2xy+y^2-MarchLight MarchLight Mathematics High School answered How to solve (xy)^2 (x^2 2xyy^2) 1 See answer my question is, there is no equal sign so you can't prove it Since the first sign is negative both signs must be negative The factors are (xy)(xy) or (xy)^2 Check by FOIL Firsts (x)(x) = x^2 Outers (x)(y) = xy Inners (y)(x) = xy Lasts (y)(y) = y^2 combine the middle terms (xy)(xy) = 2xy x^22xyy^2
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First, you want to expand the equation so it'll be x^22yxy^2=x*22xyy^2 Then you subtract y^2 from both sides x^22yxy^2y^2=x*22xyy^2y^2 After that, you simplify x^22yx=x*22xyDetecting a perfect square 12 x2 2xy y2 is a perfect square It factors into (xy)• (xy) which is another way of writing (xy)2 How to recognize a perfect square trinomial • It has three terms • Two of its terms are perfect squares themselves • The remaining term is twice the product of the square roots of the other two termsSolution for x^22xyy^2=0 equation Simplifying x 2 2xy y 2 = 0 Reorder the terms 2xy x 2 y 2 = 0 Solving 2xy x 2 y 2 = 0 Solving for variable 'x' Factor a trinomial (x 1y)(x 1y) = 0 Subproblem 1 Set the factor '(x 1y)' equal to zero and attempt to solve Simplifying x 1y = 0 Solving x 1y = 0 Move all terms containing x to the left, all other terms to the right
Gold Member 4,540 581 (xy) 2 = x 2 2xy y 2 >= 0 You know that already So x 2 xy y 2 >= xy If x and y are both positive, the result is trivial If x and y are both negative, the result is also trivial (in both cases, each term in the summation is positive) Foil out the left side of the equation (xy) (xy)=x^2xyyxy^2=x^22xyy^2 Hope this helps! LHS (xy)^2 = x^2 2xy y^2 RHS (xy)^2 4xy = (x^2 2xy y^2) 4xy =x^2 2xy y^2 4xy =x^2 2xy 4xy y^2 =x^2 2xy y^2 Hope, this may help you Mark as Brainliest, plz kaypeeoh72z and 44 more users found this answer helpful
That is, (1 xAbove proof would be \If 2xy xy p xy then 0 (x y)2," which is true but not what we want to prove (we want to prove the converse) Remember that proofs are meant to be read If you cannot read your proof aloud so that your logic is understandable, it needs work Also for fun, one student found a nice proof of the inequality that also involves squaring both sides let A = 2xy xy and let B =Factor 2x^2xyy^2 2x2 − xy − y2 2 x 2 x y y 2 For a polynomial of the form ax2 bx c a x 2 b x c, rewrite the middle term as a sum of two terms whose product is a⋅c = 2⋅−1 = −2 a ⋅ c = 2 ⋅ 1 = 2 and whose sum is b = −1 b = 1 Tap for more steps Reorder terms 2 x 2 − y 2 − x y 2 x 2 y 2 x y
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Free PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystepYou are being tasked to prove A > B A is x >= 0 and y >= 0 B is (xy)/2 >= sqrt(xy) If you are studying proofs and real numbers, I doubt that at this point you need to prove that (as picado said) z 2 >= 0 for z real number If you have seriously not encountered this yet, then you must do so Thanks for contributing an answer to Mathematics Stack Exchange!
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Click here👆to get an answer to your question ️ Verify x^3 y^3 = (x y)(x^2 xy y^2) using some non zero positive integers and check by actual multiplication Can you call theses as identities? \(\frac{dy}{dx} = \frac{y^2x^2}{2xy},\) This is a Homogeneous DE Therefore, put y = vx and \(\frac{dy}{dx}\) = v x \(\frac{dv}{dx}\) to convert itConsider x 2 y 2 x y − 2 2 x y as a polynomial over variable x Find one factor of the form x^ {k}m, where x^ {k} divides the monomial with the highest power x^ {2} and m divides the constant factor y^ {2}y2 One such factor is xy1 Factor the polynomial by dividing it by this factor
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2 x is a function of y 3 x and y are both functions of some variable (call it t) 4 x is a constant 5 y is a constant Setup Assuming y is a function of x 2 Assuming x is a function of y It's just the same steps as number 1, but with y and x replaced, sinceCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyI need to prove using the $ \epsilon\delta$ definition that $ $ \lim_{(x,y)\to(7,2)} x^2 y^2xy=39$ $ So I begin by rewriting the absolute value $ $ \mid x^2 y^2 – xy 39 \mid = \mid (x7)(x7) (y2)(y2) – (x7)(y2) 2(x7) 7(y2)\mid$ $ Using the triangle inequality, we have $ $ \leq \mid x7\mid Continue reading "Proving that $\lim_{(x,y)\to(7,2)} x^2 y^2xy=39$ using only
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But avoid Asking for help, clarification, or responding to other answersPolynomial identities (short multiplication formulas) (x y) 2 = x 2 2xy y 2 (x y) 2 = x 2 2xy y 2 Example 1 If x = 10, y = 5a (10 5a) 2 = 10 2 2·10·5a (5a) 2 = 100 100a 25a 2 Example 2 if x = 10 and y is 4 (10 4) 2 = 10 2 2·10·4 4 2 = 100 80 16 = 36 The opposite is also true 25 a 4a 2 = 5 2Steps Using the Quadratic Formula { x }^ { 2 } { y }^ { 2 } 2xy=0 x 2 y 2 2 x y = 0 All equations of the form ax^ {2}bxc=0 can be solved using the quadratic formula \frac {b±\sqrt {b^ {2}4ac}} {2a} The quadratic formula gives two solutions,
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