117. Let F(x) = x/x2 – 1– 2 Prove that F(x) and y = cosh-x differ by a constant by showing that they have the same derivative. Then prove they are equal by evaluating both at x = 1.

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

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Q: Determine the derivative of the following function: f(x) = 3ecos(3x) cos(3 x) O 9e cos(3 x) O…

A: f(x) =3ecos3x differentiating function with respect to x

Q: 4. Use the definition of derivative to compute the derivative of the following functions at x 1: a.…

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Q: 2ƒ(x), x = 2

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Q: Find the derivative of the following function g2 F(x) = ds a 3+ 5s4 using the appropriate form of…

A: Given that,

Q: Suppose that the first derivative of f(x) = is approximated by the following formula %3D 3x+4 -2f(x…

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Q: c) If f'(x) =3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the…

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Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: If f(x) is a continuous function on [3,7] and F(x) is an anti-derivative of f(x) such that F(3)=7…

A: Given :f(x) is continuous function 3,7Fx is anti-derivative of fxF3=7 and F7=3To determine…

Q: . Show that the following function is differentiable everywhere on R but of which the derivative is…

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Q: Suppose that the first derivative of f(x) =- is approximated by the following formula 3x+4 -2f(x –…

A: The given problem is to find the actual error of the first derivative of the function using the…

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

A: Given that: The function f(x) and its first derivative have the following values at x = 0 and x = 1.…

Q: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

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Q: 1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >1…

A: A function f is said to be continuous at a point x=a if limx→af(x)=f(a).  The left hand derivative…

Q: Suppose g: IR - IR is a differentiable function with bounded derivative, Fix e> 0 , and define flx)…

A: to show f is one one we will show that for  x1 not equals to x2 , f(x1) is not f(x2)

Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

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Q: Suppose that f (x) > 0 for all x, f(x) has a continuous derivative and that е — 1 f(-3) = 0 and f(4)…

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Q: Suppose that functions ƒ(x) and g(x) and their first derivativeshave the following values at x = 0…

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Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Starting from the definition of derivative prove that if f(x) = 1 then f'(a) = a2

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Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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Q: Find the value of K that make the functionf continuous at x=2 パ-4 マー3x+2 sin(rx) + kx + k if x > 2…

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Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: 59. Suppose that functions f and g and their derivatives with respect to x have the following values…

A: Since you have posted multiple questions i can do first question with first three subparts as per…

Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: If f(x) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9…

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Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

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Q: Use the Fundamental Theorem of Calculus to find the derivative of h(x)= (from -4 to sin of…

A: This is a calculus problem

Q: Find the derivative of the following function (2t – 1)* dt F(x) = using the Fundamental Theorem of…

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Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

Q: Suppose the derivative of f exists, and assume that f(2) = 1, and f'(2) = 2. Let g(x) = x2f(x), and…

A: Apply the product rule to find the derivative of g(x) and then substitute the given values as…

Q: Prove, by Showing all steps i that the 1. derivative of arcos x is 1-メ

A: Derivative of arccosx is -1/√(1-x2)

Q: 4. Find the second-order derivative of the following function: f(z) = log, cos z + In %3D

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Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

Q: Show that the function f(z) does not admit an anti-derivative in the domain N = C\{0}. Does it admit…

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Q: Show that the following function is continuous at x = 1 for all values of p. (px + 1, if x > 1 f (x)…

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Q: 2- By using mumerical approximation ,the value of the derivative (f'(x)) in the table is true f(x)…

A: To find the derivative.

Q: 1. Use the following formula (1) to evaluate derivative for each of the functions below: f(x+ h) -…

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Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: 2 Consider the following piecewise function: f(x) = 0 4 x²+3' Use the first principles definition…

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

Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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Q: Let f (x) = x sin x and g(x) = x cos x. (a) Show that f ,(x) = g(x) + sin x and g ,(x) = −f (x) +…

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Q: suppose the derivative of f exists, and assume that f(2)=3, f'(2)=4. Let g(x)=x^2f(x) and h(x)=…

A: The objective is to find the equation of tangent lines of g(x) and h(x) at x=2