Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2] 1.a O V8 b 0 3.cO 8 dO

Q: If we apply Rolle's Theorem to the function f(x) = 2x – 12x – 3 on the interval [1, 5], how many…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: Given f(x) = - 3x ^ 3 - 2x - 4 verify that f(x) is invertible and, if so, find the equation of the…

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Q: If f(0) = 0 and f"(x) exists for all x>0, then show that %3D f(x) f'(x) xf"(5), 0 < § < x. Also…

A: Let's find.

Q: Let f(x) = cos (x). %3D If it is true that f" (x) = x(f'(x))ª for some constant a, find the value of…

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Q: Z→ Z be such that f(x) = 4x + 2. Is f invertible, and if so, find its inverse function.

A: Given query is to find the inverse function.

Q: Show that : f(x) = x2 + x + 2 e Zg[x} is irreducible. Further, find the order of f (x).

A: Definition: 1. A polynomial f(x) ∈ ℤp[x] is said to be irreducible if and only if it has no root in…

Q: Given f (x) =r - 4r defined over [1, 3]. Using Secant :method, the first approximated root for f(x)…

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Q: Let f(x) = 2x In x. The approximation of f"(0.3) using the following formula with h = 0.1 is: %3D…

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Q: By using the demition, Calculate the dervedves of the functions |- }cx) = 4 - x* ; F'(-3) ,f'c1) 2.…

A: Differentiation is the rate of change in the value of dependent variable with respect to the change…

Q: Show that if f:R → R is odd and the restriction of fto the interval [0, co) is strictly decreasing,…

A: The odd functions are functions that return their negative inverse when x is replaced with –x. This…

Q: The range of F in F(x) = 2 sin x; - < x< 2 T is: %3D -2SF(x)SO F(x)S2 ) -2SF(x)S2 O O

A: Given:- F(x)=2 sinx  ,-π/2 &lt;x &lt;2π To find:- Range of F(x)

Q: (@) Let FOR^ → R be a Function given by F(x₁, x,...,xn) = x²₁².. X²...x² x², where ) > x ²₁ =1. Show…

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Q: Let f(x) = (x2 + 3x)e .Find the value of c that satisfies the conclusion of Rolle's Theorem for f on…

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Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: Let f(x) = x – x³ on [0, 1]. f(0) f(1) = Find c such that f'(c) = 0 or, if Rolle's Theorem does not…

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Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: let x has the p.d.f (11e-11x 0 < x< ∞ 0. W f(x) = Find m.g.f and prove that E(x) = M,(0)? %3D

A: We want to find the Mx(t) and E(x)

Q: Determine the c which satisfy the conclusion of Rolle’s Theorem for the given function and interval.…

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Q: 1 Let f (x) = ; 1 , then f (x) satisfies the - - 2 conclusion of Rolle's Theorem on 0, 1| 6.

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Q: Let f(x) =x² t2X. Find all the values of ċ in the interval [2,0] such that f (c) =0.

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Q: Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

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Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D 2- f(x,y) = Inx2 + y2…

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Q: A function f: Z x Z is defined as f(m, n) = 3n - 4m.  Verify whether this function is injective and…

A: f: Z x Z is defined as f(m, n) = 3n - 4m So, f(m, n) = f(a, b) implies, 3n - 4m = 3b - 4a i.e. 3(n…

Q: Consider the function f(x) 4x + 32x + 4 on the interval – 7, - 1]. Evaluate this function at the %3D…

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Q: Given that f(x) = 2x + cos(x) is a bijective function, find (f-')'(1)

A: The function f-1 represents the inverse of function f. Therefore, if f-1x=y then x=fy represents the…

Q: Find F as a function of x and evaluate it at x = 0, x = 1/3, and x = T/2. F(x) = cos e de F(x) =…

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Q: Find F as a function of x and evaluate it at x = 2, x = 5, and x = 8.

A: Integral formula:∫xndx = ∫xn+1n+1.dx  + c

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

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Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

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Q: Find a function fand a number al such that f(t) dt = 2/I 2+ for all a > 0). f(x) = a =|

A: Given that : 2+∫axf(t)t2dt =2x ,         for all x&gt;0 We need to find the function 'f' and the…

Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

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Q: For the given functions f(x), let x, = 1,x1 = 1.25, and x, = 1.6. Construct interpolation…

A: PART A The given function is, f(x)=sin πx For x0=1 then f(x0)=0 For x1=1.25 then f(x1)=-0.7071 For…

Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 12x - 4 on the interval [1, 5], how many…

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Q: 1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

A: To compute the L^2 norm of the given function, following the definition of the norm

Q: The domain of f(x) = /1 – I In(x) is %3D

A: The domain is the set of all possible x-values which will make the function give real y-values as…

Q: Let f(x) = cos(E) and P(x) be the interpolation polynomial of degree at most 3 which agrees with…

A: Neville’s method generates Lagrange’s approximations recursively. In Neville’s method, we denote…

Q: Q3: a) Let f : Z → Z be such that f(x) = Vx² – x + 1. If invertible, and if it is, what is its -…

A: the function is invertible if its one -one and onto. The function is one - one if f(x1)=f(x2)…

Q: If f is differentiable and non-negative on an interval I in R then /3f + 1 is differentiable on I.

A: The given statement is true. Because when f will be non negative then the derivative of the given…

Q: Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2] .a 3 .b 8 .C 8, .d 1

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Q: Given that f(x) = 2x + cos(z) is one-to-one, use the formula 1 (f ')'(z) = f'(f-"(x)) to find…

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Q: The range of the finction f(x, y) = In(-x2-+1) is %3D None of these O (-00:0] O [0; +0) O [0;1]

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Q: Consider the function f (x) = 4x1/2 2x. The domain of f is [0, 0). %3D - BIC 0.7mm HB #2 GIOam HB #2…

A: We can find the answers as below.

Q: Suppose that only the points (x,y), j = 1 ... 16, that lie on the graph y = f(x) of a function f(x)…

A: The interpolation techniques are used to establish the functional relationship between any two…

Q: inf f. is not measurable Vn. i

A: False ; is sequence of measurable functions fn is measurable then inf fn is measurable .

Q: Find the upper bound for the absolute error on the interval [xo, x4] for the Hermit polynomial…

A: Given:- f(x)=cos x x0=1 , x1=1.1

Q: Find F as a function of x and evaluate it at x = 0, x = T/4, and x = T/2. F(x) cos 0 do F(x) F(0)

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Q: Approximate the value of f"(2.156) if f(x) = 2tan(x) + %3D cos(2x). h = 0.003 %3D O -18.22610955 O…

A: Here the given function is f(x) = 2tan(x) + cos(2x)

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.