Integrate to find F as a function of x and demonstrate the Second Fundamental Theorem of Calculus by differentiating the result from integrating.

Q: Use second fundamental theorem of calculus. Find the derivative F'(x) of the function.

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

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Q: Use Part one of the Fundamental Theorem of Calculus to find the derivative.

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(æ) : Vt3 + 2°dt f' (x)…

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Q: Determine whether the point x=0 is an inflection point of the function f(x)=sinx.

A: Inflection point is the point on f(x) where the graphn changes the concavity. At this point  double…

Q: Expand each function (using the appropiate technique/formula) Compute the derivative of the expanded…

A: Derivative of the given functions by expanding them: 1) fx=x+52 2) fx=4x2-32

Q: Use definition to compute the derivative of f(x)= V3x+1. You may not use any calculus formulas.

A: Use first principle.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = | V+ 5°dt %3D -5…

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Q: Which are important types of functions are frequently encountered in calculus?

A: Important types of functions frequently encountered in calculus can be categorized as follows:Based…

Q: Use the Product Rule to find the derivative of f. f(x) = csc(x) sec(x) f'(x) = %3D

A: Topic :- Differentiation

Q: Using the definition of differentiation, find the value of f'(a) if f(x) = sinx

A: Topic = Derivative

Q: Integration is the reverse process of differentiation.

A: Given,            Integration is the reverse process of differentiation.To find : State true or…

Q: Find the derivative of the function. State the domain of the derivative. f(x) = [In(x)]6 f '(x) =…

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Q: Use second derivative test, If f(x) 4x +4 then f(z) has a local maximum at the point %3D I = -3 T= 3…

A: This question is based on maxima and minima of function.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. [5 ,3

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Q: Differentiate the function. f(x) − x - 3 sin x

A: we have to differentiate the given function f(x) =− x - 3 sin x

Q: Compute the derivative. f(x) = 7x sin (x) (Express numbers in exact form. Use symbolic notation and…

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Q: Use the Fundamental Theorem of Calculus to find the derivative of . 20 F(x) tan(t*)dt F'(x) = [NOTE:…

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Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

A: Integral is F(x)=∫4xt32dt

Q: 7 f(x) dt 3

A: Given that, f(x)=∫3x2(t23-1)7dt Now, the fundamental theorem of calculus tells us that If…

Q: Integrate to find F as a function of x and demonstrate the Second Fundamental Theorem of Calculus by…

A: Given,            Fx=∫0xt+2dt

Q: Let f be a function. Explain, using any method , as to why f(x) and f(x) + 2 have the same…

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Q: Differentiate the function using product rule. f(x) = (2x³ + 5x) cos x %3D

A: Given : fx=2x3+5xcosx

Q: f(x) = (2x3 + 5x) cos x

A: Given function is fx=2x3+5xcosx. Differentiate using product rule ddxf·g=f·ddxg+g·ddxf

Q: Consider the function f(x, y) = ye#Yta. Find all critical points of f and classify them according to…

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Q: Expand each function (using the appropriate technique/formula). Compute the derivative of the…

A: "Since you have asked multiple questions, we will solve the first question for you if you want any…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = | V+ 2*dt 2 f'…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = t3+3°dt f'(x) =…

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Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: we have to find the second derivative of the function at the given point. f(x) = cos x2 , (0, 1)

Q: Let f(x)= x2 + sin x - 2 cos 2x. Find (f-1)'(-2)

A: Given: fx=x2+sinx-2cos2x To find: f-1'-2 Now, we know that f-1x' = 1f'f-1x

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(z) = %3D 1 f'(z) =…

A: To use the  part 1 of the fundamental theorem of calculs to find the derivative.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 12 dt f'(x) = [NOTE:…

A: From the fundamental theorem of calculus,…

Q: () Use part I of the Fundamental Theorem of Calculus to find the derivative of 17 F(x) tan F'(z)=…

A: Topic-  derivatives of definite integration

Q: Calculate the derivative 21 using Part 2 of the Fundamental Theorem of Calculus. 21

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

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Q: What is the anti-differentiation rule to be used in order to integrate the function f Vx5 dx. a.…

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Q: Derive error formula for functional relation?

A: We have to derive derive error formula for functional relation

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

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Q: Expand each function (using the appropiate technique/formula) Compute the derivative of the expanded…

A: Here we have,  a) f(x)=(x2+2x+3)2b) f(x)=(3x-2)2 c) f(x)=sin(2x)

Q: use the first fundamental theorem of calculus

A: To solve the following problem

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = / VB+1 t f'(x) =…

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Q: Assume that y is a differentiable function of x such that y^2 = x^2 + 4xsecy. Find

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Q: Use the Fundamental Theorem of Calculus to find the derivative of f(z) -dt f'(x) -

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

A: Here given function

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 12 fe) = [, (; - )". dt…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = dt 2 f'(x) =…

A: Using fundamental theorem of calculus,

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 8. = Ge -1) at f(x)…

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Q: Use the Fundamental Theorem of Calculus to find the derivative. g'(x). of the unction

A: Use simple method of funda mental theorem