Let /(x) – x + 2x+ 3x + 4 € Z). Then x = -1 is a root for /(x) of multiplicity None

Q: Use logs and implicit differentiaton to prove (root(x))' = 0.5x^(-0.5)

A: Let y = √x Take log to the base e, i.e. natural log, i.e ln on both the sides, ln(y) = ln(√x) =…

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

Q: 1. Explain why both f(x)= x³+ 1 and g(x) tions. x3+1 are rational func-

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Q: Find a point c satisfying the conclusion of the MVT for the func y(x) = 2e* on the interval [0, 5].…

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Q: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: Find the limit of the square root of (4x^(6)-x) over (x^(3)+3), as x approaches positive infinity

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Q: Write a polynomlal f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

A: Since x=-4 is a zeros so, (x+4) is a factor of f(x) Since x=1 is a zero so, (x-1) is a factor of…

Q: Express x^8-x over 2[x] and over F2[x] as a product of irreducible

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Q: Show that the IVP x" = -6x(x')3, x(-1) = -1, x'(-1) = 1/3, has a unique solution x and find the…

A: Consider the given equation. x''=-6xx'3 And the initial values are x-1=-1 and x'-1=13. Let the…

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: Find a polynomial of degree n=3 that has the given zero(s) x = −2, 6

A: A polynomial is an expression comprised of variables, their coefficients, constant, and exponents,…

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: 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 a 5 with real coe ffients that satisfies the aiven conditions. zeros of a, 5and-3; P)=4…

A: We have to find the polynomial of degree 3 with given condition.

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

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Q: Show that x19 + x8+ 1 has multiple zeros in some extension of Z3.

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Q: Find Valume x zO; Ekort the X3D2; 0 about the x- axis

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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 the multiplicity of (x-1) is 1.

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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: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| <

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Q: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

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Q: Find a root of f(x)= In (x²+3)-x2+3 with 103 accuracy.

A: Given,  f(x)=ln(x2+3)-x2+3  By bisection method , we have  f(2)=0.3862944 which is  &gt;0,…

Q: A polynomial of degree n  1 has exactly zeros ifa zero of multiplicity m is counted m times

A: A polynomial of degree n≥1 has exactly  ___________  zeros if a zero of multiplicity m is counted m…

Q: find the interval of existence in which the particular solutions of the IVP is vaild

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Q: Use the Intermediate Value Theorem to show that thefunction f1x2 = 4x3 - 2x2 - 7 has a real zero in…

A: Given: fx=4x3-2x2-7; x∈1,2 We know that for a polynomial functiony=fx in x∈a,b, if fa and fb have…

Q: Find all zeros of f(x) = x° – 4x² + x – 4. Enter the zeros separated by commas. - -

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Q: if ニ if 1-X fCx +2) = f(x) Hx f on [-3,3] and we Suppose draw the funch'on

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Q: @ f(x)= x²-3x-4 2 @ f(x) = x² - 4x +3 Show that whether f(x) reduceable Poly or not

A: The given problem is solved below in detail.

Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

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Q: 5. For z=x2siny show that 332 332 = дудхду дугдх

A: Topic = Derivative

Q: Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that…

A: Let x and x+2 be the consecutive odd positive integers both of which are smaller than 10 such that…

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

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Q: Prove that for x&gt;0 the inequality 1+2lnx≤x2 is true.

A: Inequality given in the question is: Consider the function; f(x) = 1+2ln(x)-x2 Let us find critical…

Q: Find the term of (x + +)° that does not contain x.

A: Given expression is, x+1x6. The general term is given by, Cknakbn-k. In the given expression,…

Q: A³ f2 = V³ fs 3

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: Since x^4+x-8 is a polynomial it is continuous.Answer: f(x)=x^4+x-8 is continuous on the closed…

Q: Use the Intermediate Value Theorem to prove that 8sinx = x has a solution between and a. 2

A: Let us consider a function f(x)= 8sinx-x

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: Use the Intermediate Value Theorem to show that 2х - 3 if – 3 0 has a zero on the interval [-2, In…

A: By using the Intermediate Value Theorem to show that fx=2x-3x+3  if -3&lt;x≤0-3+2 cosh x  if…

Q: Write the eguation of a sixth degree uatioN with a root of 2 with multiplicity of 2.r0ot of -3 with…

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Q: -5 -4 -3 -2 15 -30- -45 -60- -75 -90 -105- -120- -135- J 2 For the above quartic polynomial f(x):…

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Q: 22. The function In x grows slower than any polynomial Show that In x grows slower as x → oo than…

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Q: 7. Use the Intermediate Value Theorem (IVT) to show that there is a root of the equation In r = 3 –…

A: We can use intermidiate theorem in order to solve the given problem.

Q: use the intermediate value theorem to show that there is a root of x^4+x-8=0 in the interval (1,2)

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Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Q: "8 does not divide x^2– 1 if x is even". prove it directly

A: We need to prove  8 does not divide x2 - 1 , if x is even. OR if x is even, the 8 does not divide x2…

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

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Q: 4. Prove that f(r) = 4x³ - 8² + 2x + 1 has three real zeros. %3D

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