Let f(x) = 1+ + x² + x³ + x4 +x5. Find the remainder R3(x) = f(x) – T3(x). Find the maximum value of f(4) (x) on the interval |x| < 0.1. Justify that Taylor's inequality holds true for R3(0.1) using your result from the previous question.

Q: Verify that the factorization for f (x) = x3 + x2 + 1 over Z2

A: Given that, fx=x3+x2+1. Also ℤ2=0, 1 To verify the factorization for fx over ℤ2.

Q: If f(x)=mx3+gx2-x+3 is divided by x+1, the remainder is 3. If f(x) is divided by x+2, the remainder…

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Q: 11. Use the quadratic formula to explain why a quadratic polynomial function f(x) = ax? + bx +c is…

A: fx=3x2+2x+6

Q: 2. Determine whether each function is a polynomial function or another type of function. Justify…

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Q: Let f(x) = 4+ (5x +9)³. Find f¹(x) = (1) · (√(x − 4) – 9) Find (ƒ(2)) -¹ = (¹) · (√(x-4) – 9)

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Q: Let f(x) = 2x2 - 1 and g(x)= 1 + x². Find (f o f)(x). O x* +2x² +2 4 O 4x4 – 4x2 + 2 | 4 O 2x* + 4x²…

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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: If f(x).= x³+3x k is divided by (x +1) and the remainder is 12, then - k = -8. True False

A: Given :fx=x3+3x-k*Remainder theorem; - If a polynomial f(x) is divided by x-a then the remainder is…

Q: Given m (x) = 3x - 9 and n(x) = - 4 +2x, find 2(x) – m (x). Do not include spaces in your answer.

A: By using direct subtraction rules we can   find n(x)-m(x)

Q: Show that the function f(t)=√t+√√1+t-4 has exactly one zero in Solve the equation √t+√√1+t-4 = 0 to…

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Q: Find all zeros of f(x) = 4x³ – 20x2 + 31x value, not decimal approximations. 21. Enter the zeros…

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Q: Let f(x) = x - 6 and g(x) = 7x. Find (f+ g)(1). (f+ g)(1)= (Simplify your answer. Type an integer or…

A: As per the question we can solve it as per the rules of function

Q: - Express P(x) = xª +.2x³ + 2x² - x - 3 in terms of Legendre's polynomials

A: In this problem, we use Rodrigue's formula to express Legendre's polynomials.

Q: 5. Use the Intermediate Value Theorem to show that f(x) = 3x³ – 10x + 9 has a real zero between -3…

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