9. Let (x) and (y) be two sequences converges to c with x y for all n. Assume that f is defined for all real numbers and that f'(c) exists. Prove that {-x} converges to f'(c).

Q: x+2y-z = 2 2x + 2y + 2z = 12 x-y + 2z = 5

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Q: Prove gcd(n, n+1) = 1.

A: To prove the below expression. gcdn, n+1=1

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Q: 2. Let f be the function from {a, b, c, d, e} to {1,2,3,4} with f(a) = 3, f(b) = 2, f(d) = 4 and…

A: The given function is f:a,b,c,d,e→1,2,3,4 with fa=3, fb=1, fc=2, fd=4 and fe=2.  To find : (a) The…

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Q: Which of the following is the orthogonal trajectories of the family of ellipses 2x² + y² = a? xy = C…

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Q: 11. Find an orthonormal basis for the solution space of the following homogeneous system of linear…

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Q: x 211 26 (6) Solvei (D²76y ++8) y=x+2²n + sinhn

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Q: Find the interpolating polynomial for the function f(x) = e through the points x = 0, 1, 2.…

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Q: 4. Is the following sequence convergent? Explain why. tn = n+2 n(n+1)

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Q: Determine the value of z in the below equation, giving the answer in the form x + yi. z 8 i (7 + 2z)…

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Q: Consider the graphs of f(x) = √√√x + cos x and g(x) = √√x + sin x over 13п the interval 0, . Answer…

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Q: Let p(x), g(x), r(x) be the following expressions: p(x) :: : x² - 7x + 10 = 0 q(x): x² - 2x - 3=0…

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Q: Which of the following is or are example/s of deductive reasoning? * L. A number is a neat number if…

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Q: Decode the number using the given private key. Decode the number M = 15 using the private key d = 53…

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Q: Given Show that the Fourier series for f(x) is π² f(x)= +2 6 (-1) n² n=1 -^≤x≤0 0≤x≤T 2 Σ(-1*¹.…

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Q: ) A complex number is purely ________ if the real component is equal to zero (b) A complex number is…

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Q: Simplify 3k(cos2 theta + cos theta)

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Q: Find the volume of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

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Q: Let A E RDXE, XE REXF, B € RFXD. Computed where g(X) = tr(AXB).

A: Let A∈ℝD×E, X∈ℝE×F,   B∈ℝF×D To Compute ∂g∂X where g(X)=tr(AXB)

Q: A firm faces the production function Q = 4K0.5L0.5 where K is capital and L is labor. a. Find the…

A: Note: As per our guidelines we are supposed to answer to only 3 sub-parts Q=4K0.5L0.5 where K is…

Q: Determine the area enclosed by the curve r²=4sin(20).

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Q: What is the equation of the slant asymptote of the rational function? f(x) = 10x³-15x²+x-1 5x²-2 11…

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Q: Find an equation in rectangular co recl sec(A)

A: Given,      ρ=7cscφsecθ

Q: example of n-dimentional hypercube

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Q: 3 Find the laplace transform of et²+ e²t (2cos 3t). 16

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Q: 2. A Ferris wheel has a radius of 40 feet and is boarded in the 6 o'clock position from a platform…

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Q: Find the formula 1 [ f(x) dx = w₁f (0) + w₁f (1) that is exact for all functions of the form f(x) =…

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Q: The effect of changing the growth rate variable, r, in an exponential function. If an initial…

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Q: Determine an equation, in simplified form, for the family of quartic function with COS 3 and 2 + √5

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Q: x² whether the limit exists or not. / (x,y)→(0,0) x²+y² 3. Find lim

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Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: Given that y=x2+4x−5. We have to find the first derivative of y=x2+4x−5 at x=0 using a value of h=14…

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: 4. Is M₂ (R) a field? Justify. I 5. Show that T = = { [ ² ] 12,9₁² € R} i 2 is a subring of M₂ (R).

A: Subring of a ring

Q: SW Consider the equation 2x2y" - xy' + (x - 5)y=0 in some interval 0<x< R. (a) verify that x = 0 is…

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Q: 2. Given a cylindrical storage with 5m radius and 9m in height. If the radius is to increase by 0.1m…

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Q: Let matrix T be T= [124] 364 and let vectors u and v be u= 0 For each of the vectors determine…

A: We have , T = 121364 We need to determine null space of matrix T. For that , first we will find…

Q: 0 if x = y o(x, y) 1 if x #y x, y ER". The open ball in the discrete metric space R", o> is the…

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Q: √4y, y = 4 and = 0) is revolved about the line = 2 Find the volume of the solid generated when the…

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Q: Given the set X = {x € R³ : d(x, a) . True False Rationale:

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Q: Setup a cylindrical or triple integral using. Coordinates Spherical triple integral SSS (x² + y z )…

A: Given ∫∫∫Sx2+yzdV Where S is the solid lying below the cone z=x2+y2 above the plane z=2 and inside…

Q: Given f(x)=√x-5;x+5 and g(x)=x+3. Find the domain of (gof)(x)? O All real numbers greater than 5.…

A: Here given that f(x)=x-5 x≠5 and g(x)=x+3. We have to find the domain of g∘fx.