Prove that the identity function is differentiable at every x E R

Q: Consider the function if a<0 2 + I if0<I < c, g(x) = if a c where c is a positive constant. Show…

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Q: find F as a function of x and evaluate it at x = 0, x = π/4, and x = π/2.

A: The given function is Fx=∫0xcosθ dθ . This impulse that, Fx=∫0xcosθ dθ=sinθ0x=sinx-sin0=sinx-0=sinx…

Q: Find f(x) if f°(x)=cos x with f(0) =1, f'(0) = 2 , and f'(-)=3.

A: Keep on integrating we are end up with an answer. For those constants we need these initial…

Q: Let f(x) be given by the function f(x) = { 9(x)+a, 13 – b cos x, where a and b are constants x > 0'…

A: To show that f(x) is continuous at x=0

Q: let a function f(x ) be given by f(x) = log(n+x) log(e+x) prove that the f(x) is decreasing on…

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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: Let f(x)  = tan x . Show that  f(0)  = f(π)   but there is nonumber c  in  (0, π)such that f'(c )…

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Q: problem in photo attached

A: We need to find the derivative of the given function,

Q: Let f(x) ∈ R[x]. If f(a) = 0 and f '(a) = 0 [f '(a) is the derivative off(x) at a], show that (x -…

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Q: Let f(x) sin x g(x) = x2 + 3 %3D %3D Evaluate the composite function (f og)(x)

A: Given:       To determine: (fog)(x)

Q: Consider the function Evaluate the definite integral f, f(x) dx f(x) A 2 X if x 2

A: The function is given by fx = 2if x&lt;2xif x≥2 To evaluate: The value of the definite integral…

Q: Consider a map f :R → Rdefined by: f(r) = x – log(1+e*). Show that it is not a contraction and has…

A: The given map is fx=x-log1+ex. We have to prove f is not a contraction and has no fixed point.…

Q: please explain using this theorem, why F(x)= (2x^2 - x - 1) / (x^2 + 1) is continous at every number…

A: consider

Q: Show that the functions f (x) = I x I and g(x) = x 1/3 are not differentiable at x = 0

A: Derivative of x at x=0:   Plotting: x,  xx

Q: Use the Intermediate Value Theorem to show that f(x) = cos^−1 (x) − e^x has a zero in the interval…

A: The Intermediate Value Theorem: If f is a function which is continuous at every point of the…

Q: Find the function f(x) such that f''(x) = x + cos(x), f(0) = 1, and f'(0) = 2.

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Q: In Rolle's theorem ,If f(x) = tanx be a real valued function in [0, r],then theorem %3D A. exist B.…

A: To Determine: in Rolle's theorem,if f(x) be a real valued function in interval [0,π] Given: we have…

Q: Determine whether a given function is homogenous or not homogenous: 1. f(x,y) = sin x 2. f(x,y) = x…

A: Since there is a mistake in third question i do first two question as per our company guidelines…

Q: If a function f is not differentiable at x = a E R, then f is not a differentiable function. True O…

A: The given statement is if a function f is not differentiable at x=a∈ℝ, then f is not a…

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: To find the derivative using fundamental theorem of calculus.

Q: Show that the function is continuous. f(x) = cos(x 2)

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Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

A: If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

Q: 1. Check the continuity and differentiability of the function f(x) rež x # 0 1+e* 0, at x = 0. x = 0

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Q: 1) Suppose that f(x) is a function such that f(0) = 3 and f'(0) = -3. Let h(x) = f(x) tan r. Find…

A: Given  f(0)=3f'(0)=-3 Let h(x)=f(x)tanx

Q: Suppose that f: R → R and g : R → R are related by the formula f (x) = g(x)+(x-a)". For which values…

A: Note: A function fx is tangent to the function gx at a point x=a if (1) fa=ga, and (2) f'a=g'a

Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = [ cosr' dt

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Q: Use the Second Fundamental Theorem of Calculus to find F'(x). F(x) -TVea+3 dt F '(x) =

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Q: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

A: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

Q: Consider the following. X, F(x) = %3D -5 (a) Integrate to find F as a function of x. F(x) = %3D (b)…

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Q: Determine the domain of the function f(x) = In(ln r) + x

A: f(x) = ln(ln x) + x f(x) is not defined if ln x &lt;= 0 [as then ln(ln x) is not defined] ln x &lt;=…

Q: If f(æ) = (In(x))' then: f' (x) %3D f'(e*) %3D

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Q: Express the function in the form  f ° g   F(x ) = cos x2

A: Given that, F(x) = cos (x^2) Let us consider, f(x) = cos x g(x) = x^2

Q: Let f(x) ∈ R[x]. Suppose that f(a) =0 but f'(a) ≠ 0, where f'(x) isthe derivative of f(x). Show that…

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Q: Determine if a function f : [0,2π] →R  defined by f(x) = sin 2π is continuous

A: We need to determine if a function                f : [0,2π] →R  defined by f(x) = sin 2π is…

Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = cosr' dt

A: In this question we have to find F'(x).

Q: Find the value/s of a such that the function f is continuous everywhere.

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Q: Prove or disprove that tan z is a surjective function, that is, for any w e C we can find some z e C…

A: Que Ans : if tanz is surjective function        then any w in C  there exist z in C such that   w=…

Q: Let h(x) = cos x and g(x) = x - l. Compute the composite functions h o g and g o h, and find their…

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Q: Prove that is a function f is harmonic =0, then - dx -Ldy =0.

A: Given function f is harmonic such that ∂2f∂x2+∂2f∂y2=0

Q: Show that if f(z) and g(z) are analytic functions that both have the same order N >0 at zo, then…

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Q: let a function f(x) be given by f(x) = log(r +x) prove that f log(e+x) (x)is decreasing on [0,0]| ]

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

Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

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Q: Consider the function f (x) = cos(x) for x ≤ c f (x) = ax +b for x > c (i) Give the condition on…

A: Solve the following

Q: Suppose F(x) = e¬“ dt. Find a formula for the function F(x*) expressed using an integral. 14 F(x*) =…

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Q: Suppose that f:I → R and g:I R are differentiable at ce I. Prove that if k E R, then the function kf…

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Q: / Let f: R → R be a differentiable function with the property that f(-x) = f(x) for all x E R. Prove…

A: Let f:ℝ→ℝ be a differentiable function with the property that f-x=fx for all x∈ℝ.   To Prove:…

Q: A function f is defined by f (x1) = / Cos(x – t) os(x-t) dt cos(t) f (x) : 01 Simplify f(x) and…

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Q: B) Show that f(x) sin for x * 0. for x= 0. is not continuous.

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Q: Let f : (0, ∞) → R be defined by f(x) = ln x. Prove that f is 1-1.

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