1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)-- a. dx b. V1-

Q: 1- Compare the results of the closed and open Newton-Cotes formulas when approximating a) x In x…

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Q: Show that d (x + 1)? 1 (을 tan 'x + t In dx (1 + x)(1 + x²) x? + 1

A: The given function is

Q: Step by step

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Q: Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x –…

A: "Since you have asked multiple questions, we will solve the first two questions for you. If you want…

Q: x sin 10x dx

A: Given: ∫xsin10xdx

Q: Use the Fundamental Theorem of Calculus to find (2 + cos x) dx.

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Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – 2) =…

A: Given: Let z be defined implicitly as a function of x and y by the…

Q: Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

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Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

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Q: Using the second part of the fundamental theorem of Calculus, evaluate S. 4 3 |x' – 3x dx. Show all…

A: To find

Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: b) fex-c - cos x + 1dx

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = In(2 + sin(x)), 0 <x < 2n…

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Q: Evaluate the following. x2 - x 1 dx J1+3x2 – 2r3 CO 2 dx 1+2 sin a x2 +2 dx r+1 2)

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

A: Please rate

Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: 15. Evaluate f e sin2x cos 2x dx A. 2ecos 2x + C C. 2e sin 2x В. + C 2ecos 2x D. 2esin 2x + C

A: You need to have the idea how to use substitution in integration.

Q: d/dx[(sin x)/(1 - 2cos x)] = (cos x - 2)/(1 - 2cos x)² %3D Select one: True O False d/dx(xe2X) =…

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Q: 9. Differentiate y = cos(x3/2 In x), do not simplify. x2-4 Using Calculus, show on which intervals…

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Q: Find and show the work for 2 (x+3)(3x+2) dx. (a) (b) SF (sin(2x) – cos x) dx.

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Q: If f(x) = 4c0s(x) , then f'(x) = %3D (A) – sin(x) 4°os(x) (B) – In(4) sin(x) 4cos(x) (C) In(4)…

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

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Q: - [² Suppose F(x)= = sin(t) dt. Use the Fundamental of Theorem of Calculus to calculate - (F(x³)).…

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Q: This question is designed to be answered without a calculator. f f(x) =cos(in x) and f' (x) = g(x)…

A: see 2nd step

Q: S sin x In(cos x) dx

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Q: 2. Use the Fundamental Theorem of Calculus Part II to evaluate each of the following: 2 +6x +. dx a)…

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Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: Which of the following is correct? e* dx = e* + C Ssine sin(x²) dx cos(x²) + C 2x dx = In(x³) + C…

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Q: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

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Q: There is a unique point a between where the function f(x) = sin x + 2 Cos a and 4 changes its…

A: Given f(x)=sinx+12cos2x Find Concavity  and Find πa

Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

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Q: In 3-Jın Evaluate the following: dx 2e*cose*dx T/3 4 sinx dx 1-4COSX 2-Jo x(lnx)² 1- Jo" x(Inx)?…

A: Given that three different types integration we solve these integration by using general formulas of…

Q: Use the Fundamental Theorem of Calculus to find:

A: Evaluate integral using Fundamental theorem of Calculus.

Q: 1. Use the Fundamental Theorem of Calculus Part II to evaluate each of the following: a) (5* +4x…

A: As per bartleby guidelines we only give first three questions answers.

Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B }sin'x + C {c}-cos'x + C {D} sin 2x + C

A: Given query is to find the incorrect option for the integral.

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: Use the second fundamental theorem of calculus along with the chain rule to find d sint dt dx 1 o…

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Q: Find the value of c that makes the function continuous at x = 0.

A: Given function:

Q: 1 Use the substitutions given to find fI+x dx; u = 1 + x + sin x dx; u = sin x cos x a

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Q: Find the first and second derivatives of each function. (a) f(0) = 3 cos(e) 5 (b) f(x) = x³sin(x) +…

A: a) f(θ)=cos θ3+5θb) f(x)=x3sin(x)+3cos(x)c) f(x)=e-3x+ln x-7x Note: Multiple parts are given, we are…

Q: d Prove, through the limit process, that (cos x) = - sin x. dx

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Q: | 10(2 sin(x)) cos(x)dx if J Ax)dx = 13

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Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.