Find k such that f(x) = x° - kx? + kx + 35 has the factor x - 5.

Q: Sketch the domain of the f(x, y) = ln((x² + x² – 4)(16 – x² – y²)) |

A: Recall:  Domain of the function:           The domain of the function is the set of all values for…

Q: (c) -7x+12x = 2 given that at t 0, x 1 and i 5

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Q: Find the particular solution determined by the given condition 314 f'(x) = 3x -6x; f(1) = -6 II

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Q: Q.4 Solve Cauchy Euler DE x³y" + 4x²y" – 5xy' – 15y = x*

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Q: Find the particular solution determined by the initial condition. f'(x) = 3x2/3 - 4x3; f(1) = - 8…

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Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²u"+xy' +(x² – !)u…

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Q: If we use the secant method on f(x) = x+x3+3 with X-2 0 and Xn-1 = 1, then Xn is_

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Q: Veridy that the approximate root of xa2 is: 1+Xn- Xn 2

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Q: : A plate whose shape is given by x 2+y 2 ≤ 1 is heated so that the temprature T(x, y) at the point…

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Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: The function f(x) = 2x³ 30x? + 54x 6 has two critical numbers. The smaller one is x = and the larger…

A: We have to find

Q: B) Find the approximate roots of the following equation: f(x) = x3 – 8 = 0, on the closed interval…

A: Roots of an equation f(x): roots of an equation are those values of x for which the function f(x) =0…

Q: For which values of c does f (x) = x2 + cx + 1 have a double root? No real roots?

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Q: Find the critical numbers of the function. a. f(x) = x³ + 6x2 – 15x

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Q: (a) Use the Intermediate Theorem to prove that Vx + Vx + 7 = 3 has a solution in the interval [0,…

A: We have to use intermediate value theorem.

Q: find the approximate root of function f(x) = 3.43x³ -6.4cos(x) - 9.61 by using the Newton raphson…

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Q: (a) Find the g.c.d of + x + 2x2 + x +1 and a - 1 in Q[r].

A: a. Given expressions are Dividing the equations: So the remainder is 2x2+2x+2

Q: B) Find the approximate roots of the following equation: f (x) = x³ – 8 = 0, on the closed interval…

A: Use the bisection method to find the roots of x3-8=0 find two points such that f(a)fb<0…

Q: Find h(0), h(x + 3), and h(-x) for h(x) = x + Vx² – 1. 2)

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Q: Find all values of a such that y = xa is a solution of y'' − 12x−2y = 0

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Q: Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

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Q: Use Horner's method to find po=2, Q(2) where f(x)= x³-2x2-5

A: the given polynomial is f(x)=x3-2x2-5 rewrite in standard form f(x)=x3-2x2+0x-5 to find the quotient…

Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: Q: Fird the root of the equation: (x+3)-x+29 By using Nowton Raphson method with iteretaion (loop)…

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Q: c(x, 1) = exp solves ac(x.1) a'cx.1) at

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Q: Use the variation of parameters to find the solution to the IVP. 0 1 et 1 X' (t) = x(t) + ,and X(0)…

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Q: Find the convolution of (a) Ila * IIa. (b) f(x) * f(x), where f(x) = e-l=l, -0 < x < o. %3D

A: Convolution : The convolution of two functions f(x) and g(x) is given by f(x)*g(x)=∫-∞∞f(y)g(x-y)dy…

Q: Suppose that z = 3 – i is a root of the equation - ax" + bx + cx + d = 0, a,b, c, d E R

A: given one root of the equation ax7+bx4+cx+d=0. a,b,c,d∈R is z= 3-i we know that complex roots occurs…

Q: 8. f (x) = x² – 6 , Po = 3 and p1 2 then by secant method p2 is

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Q: Given h(x) = sec(-4x2 – 3x + 2), find h' (x). Provide your answer below: W'(x) =

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Q: The function f(x) = x²e*- ex has a root in [0,2]

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Q: Find the critical numbers of the function g(x) = (x2−16)1/2.

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Q: Find the value of x. x+1 M K in

A: In the given fig, we have two triangle ∆LMK an equilateral triangle And  ∆ JMK  an isosceles…

Q: For which values of c does f (x) = x 2 + ex + 1 have a double root? No real roots?

A: Given quadratic equation is Comparing it with , we get A=1, B=c, C=1 Now, The given quadratic…

Q: Given that f(z) = (z+ 2)(z²z+4) Find f(1 - 2i)

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Q: 3. Given the function f(x) = 4x^2 + 10x + k, find k when f(x) is a perfect square.

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Q: Use variation of parameters to pind Yr F -2xy' +ay: -12 x) given that = x and Yx art solutions of…

A: Let's find.

Q: Q1: Solve the equation f (x ) = x e* -1=0 , by Bisection method where k=2.

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Q: The function f(x) 223 42x? + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Let's find.

Q: The function f:R R satisfies the condition mf(x-1)+ nf(-x) =2|x |+ 1. If f(-2) = 5 and f(1) =1, then…

A: Introduction :Given ,function f: R-&gt;R Which satisfies the condition mf(x-1) - nf(-x) = 2|x| +…

Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

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Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

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Q: If G(x) = S T/1+tdt, then G'(3)

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Q: Find the value of k so that the value of (2y - 1) dy is 10.

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Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]

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Q: Find the value of c guaranteed by the Intermediate Value Theorem. x²+ 5x 9. 18 Ke) = 18 f(x) = f(c)…

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Q: find the maximum and minimum values of f(x,y)=x3+3xy2-3x2-3y2+4

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Q: t = x+ y Use the substitutions : to solve the S = x ди ди PDE : -2y 0, u(x,2x+1) = e. -- дх ду

A: Given PDE, ∂u∂x-∂u∂y-2y=0,   ux,2x+1=ex To find the solution of the PDE.

Q: Find two consecutive integers m and n such that a solution to f(x)=0 is in the interval (m, n),…

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