Q: Use Lagrange's Formula to Prove that : 1) Y = Y3 – 0.3 * [ Y5 – Y_3] + 0.2 * [Y_3 – Y_5] . -

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: 3. For the function g(x) = x³ – 2x? – 11x + 12, use long division to determine whether each of the…

A: we devide the polynomial by given factor and if we get remainder zero then this given factor is…

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

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Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: Find the critical numbers of the functions. a) f(x) — х2 + 4х b) f(x) — х3 —7x? — 5х с) f(x) 3 2x3 -…

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Q: Find the roots of following equation: a. f(x) = 2x²1⁹ + 3x74 + 2x57 + 3x44 in F4 b. f(x) = 3x⁹8 +…

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Q: 4. Find the zeros of f(x) = x² + x – 3.

A: We know that, for a quadratic function fx=ax2+bx+c, the zeros of of fx is given as x=-b±b2-4ac2a…

Q: Determine the value and location of any inflection point of h. Enter the solution in (x, h(x=…

A: Given function is Now differentiating it twice we get  Noted that there is no x for which  , In…

Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c>0. No sign change, by Descartes rule of…

Q: The values of a and b, for which the function f(z) = x³ + axy² + i3x?y + iby³ is analytic, where z =…

A: Given function is f(z) = x3 + axy2 + i3x2y + iby3 by comparing f(z) = u +i v here u = x3 + axy2  and…

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: ] Prove that the equation 2" – x = 1+ 4/x has a solution greater than 0.

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Q: If y² - xy = 1₂ prove that: (2y-x)³ g -2=0,² is the second deravitive of y. Since y

A: The equation: y=f(x) can be differentiated with respect to x to calculate the equation of y'. The…

Q: 6. (x – 1

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Q: Express ƒ(z) = 4x² + i4y² by a formula involving the variables z and ž.

A: Let,

Q: Q: Let f: R→R be given by f(x)= x +3 Find (a){x: f(x)= 28} (b) The pre-image of 39 and 2 under f.

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Q: b. y = 3x2 - 18x + 24 Fa

A: We have given equation  (a) y=x2+2x-15 y=x2+5x-3x-15 y=xx+5-3x+5 y=x-3x+5 To get x-intercepts , put…

Q: 1. Consider the function: x3 − 6x2 +11x − 6. This function has three roots at x* = 1, 2, 3. 1. a)…

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Q: (x) - provided

A: To fill the given blanks.

Q: Answer for b

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Q: Q3) prove that: fa+¹h f(x).dx h 2h 4h - = 3 [ƒ (a) + f(a + 4h)] + f(a+2h) + [f(a+h) + f(a + 3h)] 3 3

A: Introduction: Numerical integration is a word utilized in evaluation to explain a set of strategies…

Q: 5) Use the Intermediate Theorem and Roll's Theorem show that there is exactly one root of the given…

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Q: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

A: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

Q: M- 03. Determine the real root of f(x) = -26 + 85x – 91x? + 44x – 8x* + xS: a. Graphically. b. Using…

A: The bisection method performs iterations on the midpoint of an interval to approximate the root of…

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}