(a) Show that (x2 + v2x + 1)(x² – v2x + 1) = x* + 1.

Q: if y3-3ax2+x3=0,then prove that y2+ 2a2x2y-5=0

A: Let dy/dx= y1 and d2/dx2=y2 And We will use the product rule of differentiation.

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: Show that f(x) = (3x + 2)/(5x-1) is invertible. Determine the domain and range of f and f-1.

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Q: What is the value of f(2) for the polynomial x ^ 3 + 3x ^ 2 - x + 1 ? What does this mean about the…

A: Here, fx=x3+3x2-x+1

Q: 9. Integral (2x-5) ai x² = 5x + 3 -

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Q: Min z = 4x1 + 2x2 s.t. 3x1 + x2 ≥ 27 -x1 - x2 ≤ 21 x1 + 2x2 ≥ 30 x1 and x2 are unrestricted .

A: the given LPP is as follows Min z=4x1+2x2 subject to  3x1+x2≥27-x1-x2≤21x1+2x2≥30 where x1,x2 are…

Q: )х, х(0) 5 8 -1 -2 X(0) = X' = %3D X(t) = || %3D

A: To find: The value of x(t) Given information: x'=8-156xand the initial condition is x(0)=-26.…

Q: Consider the funciton f (x) = -(x – 1)²(x + 2)³ (x – 3). 1. 2. State all zeros and their…

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Q: 2. Let h(x) = |9 – x²].

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Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

A:

Q: Express the polynomial x3 + 2x+3 EZ-[x]as a product of irreducible polynomials of 75[x].

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Q: 9. For |x|<1, prove that 8x 16x 24x 1-x1+x 1-x 2 8x 8x = 1+ (1 – x)? (1+x2 (1-x)? ...

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Q: Find the inter val of Valiediy -2x=2 ১০) - 2.

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Q: Verify that f(x)=x3- 3x + 2 satisfies the hypotheses of the Mean Value Theorem on the interval…

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Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1 A True False

A: We have to state whether the given statement is true or false and its reason is given.

Q: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: Given is a expression  1215-x&gt;24-2x2. It is required to prove the given expression for all…

Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of f-1

A: fx=2x-18 Now consider, fx1=fx2,                   where x1, x2∈ℝ⇒2x1-18=2x2-18⇒2x1=2x2⇒x1=x2…

Q: 29. For |x|<1, prove that 24x 1-x 16x 8x 1 + 1-x1+x ....... 8x &r = 1+ (1- x) (1 +x)2 ' (1-x)2 ...

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Q: 18x- 2(3x + 1) = 5x – 16; Prove: x = -2 %3D

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Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y -5=0

A: Our objective is to prove y2 + 2a2 x2 y -5=0 if  y3 -3ax2 +x3 =0. But note that when a=0 and x, y=3,…

Q: Q1. Find the general solution for the non-homogen 1st OLDE using undetermined coefficient method.…

A: Given Y'=-3-456Y+5-6ex

Q: 2y = xx -1-In(x+vx² -1)+c

A: Given the family of curves is 2y=xx2-1-lnx+x2-1+c. Find the orthogonal path of the above curve.

Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: fo)-글x3-글 x2-6x +4 has

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Q: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

A: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5=0

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Q: 2. Identify the approximate input values of any relative maximums and minimums of this 5th degree…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find Absolute Extremums of F(x)=2x^3-6x over [0,3]

A: To find the absolute extremums of the function F(x)=2x3-6x over [0,3]

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5 =0

A: Given : y^3 - 3ax^2 + x^3 = 0

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: II) Classify the PDE (1 + x)²Uxx - 4xUxy + Uyy = x.

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Q: If y3-3ax2+x3=0,then prove that y2+2a2x2y-5=0

A: Solution of this question is

Q: y3-3ax2+x3=0,then

A: Given:  y^3 - 3ax^2 + x^3 = 0

Q: 4. Find the maximum value of x if f(x)=6cos(x)-3x²-2x. Using Quadratic Interpolation with a relative…

A: Solution...

Q: 1. Find the first-order derives: III. y = (2x* – 5)(3x5 + 12) IV. V4x? + 7+ 5-x° + 15x – 30 5x+ 4x3

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Q: 3 13. Evaluate x2 Vx + 2 da -1

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Q: A polynomial which goes through the point (1,4) and has zeros at x=0,x=3 and x=-2

A: Given:A polynomial pass through the point (1,4) and has zeroes at x=0, x=3 and x=-2.

Q: Evaluate A (z 2") by parts.

A: Solution:

Q: 3. A polynomial of degree n 21 has exactly a zero of multiplicity m is counted m times. zeros if

A: To fill in the blanks where statement is A polynomial of degree n≥1 has exactly ......... zeros if a…

Q: n decomposition for (x+2) (x – 3) -

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Q: Find the sum of all the critical numbers of f(x) = 2x3 +3x2 – 36x +8 -

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Q: Find the critical number of f(x) = 3x^2 - 18x + 4

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Q: 2/3 of f(x) = (x²4)73. (b) Find all critical nurabers

A: There are multiple question. As per company policy kindly ask other question separately. b.

Q: Eliminate the arbitrary constants of: x^2=Axy+By

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Q: What is the zero-product principle?

A: Zero product principle states that if ab=0  then a=0 or b=0 We apply zero product principle while…

Q: 2)Let PCv) =x" -5x 74 A. find all Possible rotional Zeros b, find Compiete factorizatin Of p C. find…

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Q: 6. Find all real solutions to V3x +1+ V9x + 4 = 11. Show your work!

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Q: Find 2 for all of: 1- y = xvInx 2- y = 3 x(x-2) x²+1

A: