Consider the identity function i(r) = I. Use the definition to prove that i'(P) = 1 for all peR.

Q: Let F(u, v) be a function of two variables. Find a formula for f′(x) when             (a) f(x) =…

A: Given fx=F4x-4hence u=4x , v=4f'x=∂F∂u.∂u∂x+∂F∂v.∂v∂xBy chain rule      =∂F∂u.∂∂x4x+∂F∂u.∂∂x4…

Q: Construct a divided-difference table

A: Given  Based on the five points . 1st order differences 2nd order differences  3rd order…

Q: Find the smallest interval in x over which the functions sin(x/xo) and cos(Tx/xo) are orthogonal. On…

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Q: y = In[sin(x + y)]

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Q: Test the sets of functions for linear in­dependence in F For those that are linearly dependent,…

A: Given: A set of functions is 1 , sin2x , cos2x. To Find: If the given set of functions are linearly…

Q: Find the x-coordinate of the point on the graph of f, between points P and Q, at which the line…

A: Let (x,y) be the point at which the tangent to f(x) is parallel to line PQ.

Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

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Q: 4. Let a be a real number such that 0 < a < 1, and let f(t) = eat – t where t e R. a) Find the…

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Q: Let y = tan10 (x5).Find ƒ, g, and h such that y = ƒ(u),where u = g(v) and v = h(x).

A: The given function is

Q: Let a(x) = -=-31(x - ²) Σ where I is the unit step function. Evaluate and So da [xdxx ada

A: As per the question we are given the function α(x) including an infinite sum containing the unit…

Q: Describe the continuity of the function h in the interval [0, π]. Show solution and explain

A: Given Function, hz = ez sin z - sin z + cos z, Given interval : [0, π ]

Q: Let a<b. Use an important theorem to reason that t  | y(b) − y(a) | ≤ 3000(b − a).  The function is…

A: Step:- 1 Mean value Theorem :- Let f be a continuous function on [a, b] and function is…

Q: Derive the autocorrelation function of: x₁ = $xt-1 + εt + 0€t-1 assuming that p < 1, and E(?) = 0²,…

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Q: Let a be a fixed positive number, not equal to 1. Let f(x) = e-e*. %3D Find the real number x1 such…

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Q: State the set of zeros of f(x)=2sin(x)cos(x) using set builder notation.

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Q: The function f(æ) = tanh I> 0 is equivalent to which of the following functions Select one: 2x -1 a.…

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Let n be a positive integer. Define the function fn(z) by dn dzn Find the value of fn(-1+i).…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: a) Express the function shown in terms of unit step function and obtain its L.T. f(t)

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Q: Find the definition set of the following function F(x)= √ln(sinπx)

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Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

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Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

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Q: Write f(x) in terms of unit step functions, Ua(x).

A: Consider the equation

Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: show that the following function analytic f(z) = 4e²+ Sin Z arp

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Q: Qs, find Thi domain of He function

A: Given the given function is fx=1-x. Domain→it is the set of input values at which the function is…

Q: Consider the following functions: (i) z = arctan (-) -(√) (ii) z= In (iii) z = (ex-ex) sin y. Which…

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Q: Show that sin x < x for all x ∈ (0, 2π).

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