4. 7. Suppose f(x)dx = -6, f(x)dx 6, and g(x)dx = 2. Evaluate the following integrals. 2 ... Jgndx = %3D 7. (Simplify your answer.) Jogwar - 6g(x)dx = (Simplify your answer.) [g(x) – f(x)]dx = | %3D (Simplify your answer.)

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: Find your answer below

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A:

Q: By writing the summation of the two power seriesE 2nc, x"+ E 6c,x* 0, we obtain: Ze + o[2(k + 1)ces…

A: We have: ∑n=1∞2ncnxn-1+∑n=1∞6ncnxn+1=0...(1)

Q: (x + y) dx dy dz =? Select one: 9. O 1 O 5 None of them

A: Topic = Integration

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A:

Q: Using two or more complete sentences, explain how to find the sum of the geometric series. n-1 4 n=1

A: Infinite gp

Q: Work Problem . } solutions and justify your answers. : Write step by step 1), Consider the DE x²y" –…

A:

Q: 3y + 2y Solving by variation of parameter y" Wronskian W is: 3e*cosx, the value of |

A:

Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x -…

A: Given that f'(x)=x-12x+2

Q: Evaluate the limits lim 5x+ 6. undefined

A: We will find the limit.

Q: 10. Create examples of functions (and also justify why it works for each): a) Continuous and…

A: As per bartleby guidelines we are supposed to answer only 3 subparts of a particular question. This…

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A: The solution for the question has been provided both on paper and on the graphing tool desmos for…

Q: degrees

A: We will find the degree of freedom.

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A: Second-order linear equations with constant coefficients. The generic form of an equation like this…

Q: -3 < x To nenen Is fox is odd ? even or

A: Use definition of odd and even .

Q: dy Find the general solution for: -6y dx Select one: O y=C.e¯z О у y = C. e-6x O y = e-6x O None. O…

A:

Q: Find the angle in radians for the given right triangle. Round answers to the nearest hundredth. 10 7

A: Given angle to find is θThe side opposite to θ is called the Opp side and the side that is longest…

Q: Arcsin(x/y) = 4x + 3y %3D

A:

Q: Using appropriate substitution, S [sec³ (2x) – 2] tan(2x) dx is equal to

A: integration

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A: We are asked to find whether is exact or separable or  homogenous equation.

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A: Given, y'=y ⇒y'-y=0

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A: From integral test of a series we get,   If a function f(x) is continuous , positive and decreasing…

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A: This problem gives us the system of linear simultaneous equations. This system can be represented by…

Q: Using decomposition into partial fractions, 4x2 + 2 dx x(x2 + 2) is equal to In/x (x² + 2)| + C…

A:

Q: What is the coefficient of the second term in a binomial that is raised to the sixth power? 5 15 20…

A:

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A:

Q: 1 f(x) X - 9 Determine whether f(x) approaches ∞ or -o as x approaches 9 from the left and from the…

A:

Q: On the circle x² + y² = r², find y". r2 A. y" C. y" = y - x3 E. None of these -x² - y2 В. у" D. y" :…

A:

Q: Given f(x,y, z) = In(x² + y² + z²), show that ² f , ²f , ² f x² + y2 + z2

A: Given problem:-

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A: Given    Angle C = 100°   Side a = 3 yards    Side b = 8 yards

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A:

Q: Ssin ³xcos³xdx

A:

Q: 4 8. + 6. 16 Consider the following geometric series: 2+ + .... Identify a and r, find a formula for…

A: The given series is  2+4/3 +8/9 +16/27+...

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A: Topic:- application of derivatives

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A:

Q: 2x+3 (a) Given f(x) = and g(x) = , determine (g f 1-x

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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A: here figure 1  is pependicular line because given that both intersect at 90 degree    in figure 2 is…

Q: O O O O For the differential equation (x2-4)y" + (x-2)y'+ 2y 0, a regular singular point is: O x-4…

A:

Q: Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity…

A:

Q: Use substitution to determine whether the given x-value is a solution of the equation. -5 tan x= 3 O…

A: topic- trigonometric equations tan(-θ)=-tan(θ)tan(π-θ)=-tan(θ)

Q: 5. Prove lim,40 V2r +I= 1.

A: Given :limx→02x+1=1

Q: Using appropriate substitution, [sec (2x) + 1] tan(2x) dx is equal to

A:

Q: Using the substitution x = sec 0, -dx x²Vx² – 1 - where x > 1, is equal to 2vx2–1 + C x² – 1 + C X X…

A:

Q: By writing the summation of the two power series E=3 (n– 2)(n+1)c,x"-3+ En=0 Cnx" = 0, we obtain:…

A: Please see the answer below.

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is

A:

Q: A state makes auto license plates that have two letters (excluding I, 0, and Q) followed by four…

A: A state makes auto license plates that have two letters(excluding I, 0, and Q) followed by four…

Q: Sx² sec² x³ dx .2

A:

Q: The series 5 n4+ 8 In=17 n++1 is divergent. Select one: O True O False

A: Given query is to find statment is true or false.

Q: Consider this function: y=-5 sin(3x+x) (Continued from previous question.) Imagine the graph of this…

A: We will find the 5 points.