Prove that the Lagrange's formula can be put in the fom ø (x) f (x,) n P „(x) = Ë Σ %3| r= 1 (x- x,) ø' (x,) | where (x) = II (x- x,). r= 0

Q: sin x then

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Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

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A: ∫x f(x) dx=x F(x)-G(x)                                  F'(x)=f(x)G'(x)=F(x)

Q: Find the weak derivative of f(x) = |x² − x + 1/5 on the - 1) interval (0,1).

A: 1.Given: fx=x2-x+15.To Find: The weak derivative of the given function on the interval 0, 1. Note-…

Q: Using an appropriate substitution, i) Evaluate [x (1- x)³ dr.

A: The solution for the above question is as shown below.

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Q: 7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the…

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Q: Find for f'(x) | f(x) = x – cos(x) f(x) = e* – 2x - 2

A: To find f'(x).

Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

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A: Given   According to the question, the mean value of land and buildings per acre from a sample of…

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

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Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: d) Bessel function, Show that So Jo(x) dx = 1.

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Q: 4) dependent Show that the following set of functions is Linearly independent or linearly f₂(x) = 3,…

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Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: What is the domain of f(x)=cos-'(In(x))? Select one: O (0,1) O (0,0) O (0,e]

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Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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Q: x f(x) f'(x) g(x) g'(x) 1 1 1 3 3 4 3 65 1 3 -2 3 4 4-2 -6 51 6 The functions f and g have…

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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: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Let f(x)= x³+1. Then (fof)'(1)= O 20 O 36 O 3 O 9

A: Please refer to the image below

Q: 3 prove that sinh (2) isine

A: Since you have posted multiple questions, we will provide the  solution   only to the first question…

Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

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Q: P2: |(e* sin x + x In x) dx

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Q: Use the fundamental theorem of calculus to find F'(x) F(x) = r5x S COS I cos (v²) dv

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