If p(x) = p(t)dt, prove p must be the zero function. Hint: Fundamental Theorem of Calculus.

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: F(x) = (2t – 1)³ dt x5 using the Fundamental Theorem of Calculus. F'(x) =

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Q: F(x) = (2t – 1)³ dt using the Fundamental Theorem of Calculus. F'(x) =

A: Given : F(x) = ∫ x3x72t-13dt

Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: =: (1)6 In(t)dt, 1, = e.

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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: Solve for g'(x)?

A: Given:

Q: F(2) = (2t – 1)° dt using the Fundamental Theorem of Calculus.

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Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

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Q: Find the linearization of g(x) = 3 + sec (t - 1) dt at x = -1.

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Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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

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Q: Find the linearization L(x) of the function f(x)=x^3/4 at x=1

A: Given, f(x)= x³/4 x=1 Therefore, f(x=1)=1³/4 f(x=1)=1/4

Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the linearization of the function f (x) = xº at x = 1. L (x) = Using this linearlization, f…

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: let f(x) = { ax2+x+1 if x is less than or equal to 1                 { bx if x >1   find a and b…

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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 the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: Use the Fundamental Theorem of Calculus Part I to find dh/dx given h(x) = cost dt (Hìnt: need…

A: Answer:  By fundamental theorem of calculus  Let fx=∫axbx gt. dt   dfdx=gbx.b'x-gax.a'x

Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

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Q: 22. 13: Fundamental Theorem of Calculus y(x) : V1- t2 dt Find g'(x). Answer:-

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Q: (a) Find the linearization of the function f(x) =x+ at x= a=1

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Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: d. d rsinx 2t3 -t dt dx 4

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Q: III. Let g be defined by the equation g(x) = dt t²-1 Show that g'(x) = secx.

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Q: 2.Use the Fundamental Theorem of Calculus Part 1 to find the derivative of the functions 17 yt a)…

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Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: (b) Show that the function f(z) = ez, z = 0 and f(0) is not analytic at Z = = 0, although C-R…

A: The given function is fz=e-z-4=1e1z4 To show: f(z) is not analytic at z=0 and f satisfies C-R…

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

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: Find the linearization of L(x) of f(x) at x=a f(x)=StartRoot x2 +17, End Root a =8

A: Given function and point is

Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

Q: Find the linearization of the function f (x) = a° at a = 1.

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

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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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Q: F(x) = (2t – 1)³ dt - using the Fundamental Theorem of Calculus. 25 F'(x) =…

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Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Every cubic function (i.e. function of the form f(x) = ax³+bx²+cx+d with a, b, c and d constants,…

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Q: Find the linearization L(x) of the function at a. f(x) = e5x, a = 0 %3D L(x) 1 + 5x

A: f(x)=e5x point a=0

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 16

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