(1+i)" – 1. F = A[- - i

Q: 2. Express in indicated derivative in terms of the function F(r). Assume that F is differentiable.…

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Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Prove the below function is not analytic at z = 0. By calculating all the directional derivatives of…

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Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = θ + sin2 (θ/3) - 8, (-∞,…

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Q: Find the derivative of f(2) = sinh(2²) – 2z cos(32). Is this an analytic functio %3D

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: a) Differentiate f(x) = sin x from first principtes. %3D

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Q: x2 f (x) = t² sin(2t) dt 1

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Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

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Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Find Taylor s Sen'ey fer ci) f() = Sin (x) about x= | f (x) = los (x) about f(x) = about x=1

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: A boy is pushing a box with a force that can be described by the function: (x) = x³ - sin 2x + 1,…

A: Given :f(x)=x3-sin2x+1=22.688

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

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: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

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Q: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: 16. r(0) = sec 0 tan 0 – 2eº -

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Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: 1, cosX, cos 2X,--- , cos mx

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Q: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…

A: According to the fundamental theorem of calculus, the following expression is to be true if F is the…

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: 3. Use the imverse function theorem to find the derivative of f(r) = cosr. COS

A: Derivatives of inverse trigonometric function

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: , (a) Find the directional derivative of at (-2,1) in the direction u = ?-j. X.

A: Since you have asked a different question. I am answering the first one. Please post the question…

Q: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

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Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

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Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

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Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)

A: Find the derivative of function

Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

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Q: the Prove function is analytic at z = 0. By calculating all the directional derivatives of the that…

A: The given function is ; f(z) = z¯2z,if z&gt;00,if z=0 We have to show that the function f(z) is not…