Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or x^2 +xy +y^2 = 7

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A: Given, I=∫-1.224ex-3 dx To find : Integral value , I

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A: f(x)=14+x

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A: Question is solved.

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A: Note  your Question is wrong because right Question is  y=sec(x) then y' = sec(x)tan(x)

Q: The force on a particle is described by 2x3 - 4 at a point æ along the a-axis. Find the work done in…

A: The force on a particle is described by 2x3 -4 at a point x along the x-axis. Find the work done in…

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A: The given question is taken from the derivative of the function in which we have to find the…

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A: Integration

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Q: The integral of f 2rVr² - 5dx by substitution method is 3(z 5) + C 2. 2(r 5) +C 3. 3(z 5) 21 2( 5)

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Q: b) Show that 2x² + 8x + 14 = 2 (x + 2)° +3 by completing the square. Hence, evaluate the integral-…

A: Use integration rules

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Q: is Flaiy)= integrahing an 2

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A: A detailed solution is given below

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A: This question is based on Cosine hyperbola.

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A: SOLUTION-

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A: Query- How can we use the general definition to prove the theorems. Answer- A theorem is a statement…

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A:

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A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

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A: Given query is find the value of the integral.

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A: See the details solution in below

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Q: Evaluate 3x3 – 2x2 + 4x – 8 - x4 + 4x2

A: Let the given integral be I - I = ∫3x3-2x2+4x-8x4+4x2dx = ∫f(x) dxThen,f(x) = 3x3-2x2+4x-8x4+4x2f(x)…

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Q: 2an-butn Converge bey to

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A: Here, integral is,

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Q: lime

A: The epsilon-delta definition of limits:   The limit of f(x) at x = c is L if for any ε&gt;0 there's…

Q: Differentiate, and make sure to show all your work: 3z ²-2 Y= 5 cosh z

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A: We will integrate the above expression.

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