Find a function f and a real number a such that 4 + | f(t) dt = x tan -1 x. -

Q: Use Part 1 of the Fundamental Theorem of Calculus to find g(x) = 1 (a) dt t3 + 5 g'(x) = (b) h(x) =…

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Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4

A: According to question, Local linear approximation,lx = x2 +π4-12,         .......1Given Function,fx…

Q: Let F(x) Vt2 +3 dt. Find 1.

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Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

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Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: 11) Consider F(x) = S*sec t tan t dt a) Integrate to find F as a function of x b) Demonstrate the…

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Q: Use the First Fundamental Theorem of Calculus part one to find F'(x). F(x)=|, (t² +3t +2)dt J-3

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Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: Fundamental Theorem: 2z Let f(x) = | Vcos t + t° dt . Find the value of f'(x). %3D 1

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Q: If g(x) J.J S. 1 -dt , find g'(2).

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Q: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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Q: 3 62 what is 13 | f(t) dt? f(x)dx = 3 6.

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Q: Find F '(x). F(x) 3 tan(t) dt %3D F '(x) = 0

A: Given that, F(x) = ∫0x3tan(t) dt We have to find F'(x).

Q: psin(rx) (b) Let g(æ) 1 and f(x) g(t) dt. Find f'(2). x4 + 1

A: We have to use derivative under the functional limit formulae first then put x=2.

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: If f(x) • cos ( z ) t'dt then f'(x) =

A: We can find the answer as below

Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Find F '(x). F(x) = 4 tan(t) dt J- F '(x) =

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Q: 1 Find f(1) if f(t) dt = x" - x + 2x? – 2, x >1.

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Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

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: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: Find a value of x such that

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Q: If f is differentiable everywhere and f(1)=f(2)=π, then ∫12 f'(t)dt=0   True or false?

A: True because,

Q: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: 6. let h be the function defines by h(x) = 2e***dt, Find h'(2) %3D

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: ди ди + 2х. -00 1, t- 1, a + 2x- dt dx и(х, 1) %3D f(x).

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Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: Let g(x) = [" sin(t²) dt- Calculate g' (3).

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Q: 1 Find F' (0) given that F(x) : 2 dt. = r In(t+1)

A: Explanation of the answer is as follows

Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

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Q: Orthonormalize x,(t) = t ,x2(t) = t? and x3(t) = t3 in this order, on the interval [-1,1] where (x,…

A: Here we have to Orthonormalize, where the functions are {t, t2, t3} on then interval [-1, 1]…

Q: 4. Let f € L'(R). Prove that the function F(x) = S f(t)dt is continuous.

A: Let, f∈L1ℝ. Since,  L1=f:ℝ→ℂ∫ℝftdt<∞∫ℝftdt≤∫ℝftdt<∞Therefore,∫ℝftdt<∞ ∫ℝftdt is a finite…

Q: In (secx) a) | sec2t dt + cot x

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Q: | 28. For each x > 0, let G(x) = J each x > 0. e dt. Prove that xG(x) 1 for

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Q: If F(x)=[ cos(t² +1)dt , calculate using the fundamental theorem of calculus derived version.

A: Given : F(x)=∫-xxcos(t2+1)dt Aim: to calculate using the fundamental theorem of calculus ,the…

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

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Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

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Q: (a) If g(x) = (tan t)³ dt, find g'(x). (b) If h(x) = | (tan t) dt, find h'(x).

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Q: Show that the functions ƒ 1 (x) = sin x, ƒ 2(x) : = cos x, and f 3(x)=x cos x are linearly…

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