1. Show that the function p() = x + 4x3 – 9 has two real roots, that is, there exist r1, r2 ER such that ri r2 and %3D p(r1) = 0 = p(r2). (Note: Before you use a theorem, make sure that the assumptions are met.)

Q: The linearization at a=0 to √2+5x is A+Bx. Compute A and B

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Q: prove that [(1/₂) = √T by using the definition of error function.

A: We have to prove that τ12=π by using the definition of error function.

Q: The domain of the function f defined by e5x+3y+9xy5 f(x, y)= √130-5x²-5y² is equal to: In D = {(x,…

A: We are given the function all for two variable for which we need to verify if the given set is…

Q: Given a function f (x). Suppose that, the Newton's interpolating polynomial P2(x) of f (x) at the…

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Q: 2. For a, b e R, show that r3+ ax +b= 0 has three real roots iff 4a3 + 2762 < 0. Remark: This is a…

A: We have to show that, x3 + ax +b =0 has three real roots iff 4a3 +27b2 &lt;0 for any real numbers a…

Q: Determine the roots of f(x) = -12-12x+18x² -2.75x³ a. Graphically b. Using Bisection Method c. Using…

A: Sol:- -12-12x+18x2-2.75x3=0Write in the standard form anxn+… +a1x+a0=0-275x3+1800x2-1200x-1200=0Find…

Q: 3. Use the Argument Principle to show that (a) f(z) = z + 1 has one zero in the first quadrant, and

A: Given: f(z)=z5+1

Q: 7. Find the Domain of cach of the following functions. a) f(x) =2-V-4 b) f(x) =5x² - x+17

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Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

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Q: (2) The real part of Syy (@) and the real part of Syx (@) are even functions of o, i.e., Re[Sy (@)]…

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Q: 1. Let f(x,y) = (x² - y²)² . Determine the equation. when x = 0, y = 0, and y = x. 2. Find the…

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Q: Let xj = xo + hj for j = 0, 1, 2. Use the quadratic polynomial interpolating f at those nodes to…

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Q: Find the exact intersection points of the functions: f(x) = 2cos2x +5sin x- 11 g(x) = 8sin2x – 6sin…

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Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

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Q: 3. g(u) = √u+√4=u

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Q: 3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R,…

A: Note:As our company  guidelines we are supposed to answer only first 3 sub-parts. kindly re-post…

Q: 1. Let f (x) = 2x² – x – 1 and let g(x) = x – 1 Which statement is true?

A: Given, f(x)=2x2-x-1 and g(x)=x-1

Q: For a real number k, the function 3 π ƒ(x)= cos² (x − ³/n)-cos (x −7) + k 4. 4 has maximum of 3 and…

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Q: 1. Identify and sketch the domain of f(x, y) = √y² + 4x + 2 In(1-x² - y²)

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Q: 6. Show directly that inf(B) = 1 for B {N =: 4+1} -

A: The given expression is,  B = {1+1/n : n belong to N}

Q: Find the set of values of b so that the function f:R→R given by 21-4b - b? f (x) = | 1- x³ +5x + a,b…

A: B belongs to [2,3]

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ E R. -

A: Given, x.f(x-1)=x-3.f(x),  ∀x∈R put x=0 in equation 0×f(-1)=-3f(0)f(0)=0 put x=1…

Q: Construct the Langvange inter po lation polynomial for the function y= Sin Tx, taking the points %3D…

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Q: What are the imaginary roots of the function in #20? f (r) = x³ + 2x2 + + 3x + 6

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