Find all functions f so that f'(x) = 7x2 – 7/x. (Use C to represent an arbitrary constant. Remember to use absolute values where appropriate.)

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

A: To find the standard form of the equation of the hyperbola.

Q: The radius of convergence of the series 2 (n!)2 (x– 2) ² is equal to n=1 3" (2n)!

A: Given series ∑n=1∞   (n!)23n (2n)!(x-2)2

Q: Question If 4sin 0 – 9 = -7, where 0 <0 < 2n, what are the values of 0? List your answers as exact…

A: We have to find the values of θ.

Q: 5. S cot³ (40) /csc(40) de

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Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

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Q: Find the derivative of the following functions by applying "Delta Metho Show your complete solution.…

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Q: Let F be a commutative ring with identity and let f (x) E F[x] be a polynomial of degree 4. Which of…

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Q: 2. Let A = (1,0, 2) and B = (6, -2,3). Solve for proj, B.

A: As we know that; The expression for the vector projection B onto A is: projAB=B·AA2A   Given: A=1,…

Q: (cos 12t – cos 3t) dt 2 sin7t sin4t dt= A True (B) False

A: This question is based on indefinite integral and Trigonometric equation.

Q: 3. Determination of integrating factors: 2y(x+ y+2)dx +(y² - x² -4x-1)dy = 0

A: The given differential equation is  2y(x+y+2)dx+(y2-x2-4x-1) dy=0. Repost the next question.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 5. y = Arctan²(x³) 2х-1 6. y = Arccos 3x+1/

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Q: ft号+号 13 4. 4 2.

A: We can solve this as follows:

Q: Find the area of the region enclosed by the curves y=x^2 and y=6x by integrating with respect to y.…

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Q: 1. Find the Radius of Convergence (R.O.C.) and the Interval of Convergence (I.O.C.) for the…

A: Consider the power series                 ∑n=1∞ an(x-a)n then series will convergent if x-a&lt;R ,…

Q: CoS“ n In n а. n2 n³ n=1

A: Solution: a) ∑n=1∞cos2(n)n2+ln (n)n3

Q: In(tan-x) dx 1+ x²

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Q: Consider a triangle ABC like the one below. Suppose that a=50, c=68, and A=26°. (The figure is not…

A: Consider a triangle ABC like the one below. Suppose that a=50, c=68, and A=26°.To solve the…

Q: sin (20) do 2 1+ sin? (0)

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Q: (10re", 2.r3 + 3.r² – 12.r, r>0 I<0 Given: ƒ(x) (a) Identify all critical numbers of f. (b)…

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Q: Complete

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Q: Use the first derivative test to find the location of all local extrema in the interval (0, 27) for…

A: answer is in  next step

Q: | sec(/I) tan(/) dr

A: We need to solve integral.

Q: Determine if the following statement is true or false. The points P(1, 0, 1), P2(3, - 4, - 3), P3(4,…

A: Use the distance formula to determine whether given lines laying on a same line or not.

Q: Find the derivative of the following functions and simply it whenever possible. 5. y = 4x ln 4x

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Q: Determine the magnitude and direction of the vertical shift and the phase shift for the function…

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Q: The origin of a coordinate grid is labeled A. Line segment AB forms an angle of 30° with the x-axis.…

A: find the components

Q: What is the area of the region bounded by the graphs of y = æ and y = 2? Answer is in square units.…

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Q: sin x dx cos3 x – 8 - 8

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Q: 4 (3x – 4)³ dx = f(u) du a where (enter a function of x) dx (enter a function of x) = np (enter a…

A: ∫343x-43dx  ----&gt;1Substitute u=3x-4Differentiate du=3dxSince u=3x-4Substitute x=3u=3(3)-4u=5So,…

Q: 2. Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 3°, where t is given in…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i+ 6j. NOTE: Enter the exact…

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Q: ` log x dx

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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Q: Include the following information • Domain, ? and ? intercepts• Intervals of increase/decrease•…

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Q: I only need C &amp; D. I've already done a &amp; b

A: c) From the table we get take points: -3, 4.333, -2, 5, -1, 6. We plug them in the exponential…

Q: Find the mass and center of gravity of the lamina bounded by the I-axis, the line z = 49, and the…

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Q: Consider and remember that A = (0,4,2) , B = (6,-1,0), C = (3,0,1> %3D %3D 1 1) Determine the unit…

A: Here, the given vectors are: A=0,4,2, B=6,-1,0  C=3,0,1

Q: Integrate completely

A: Solution-

Q: A solid right cylindrical cement block of volume 9n ft is to be made, and then painted except for…

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Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: Consider the following function. f(x) = 3 − |x − 2| (a) Find the critical numbers of f. (Enter your…

A: The given series is: f(x)=3-|x-2|      =3-(x-2); x≥23-(-(x-2));x&lt;2      =3-x+2; x≥23+x-2,x&lt;2…

Q: Consider the point P(-2,3) on the coordinate system. Describe geometrically the position vector…

A: Given point P (2,3)

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: The head of the vector v is pointed at (7,-2) denote it by A and the tail of the vector v is located…

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Q: 3. Find the value of c guaranteed by the MVT for integrals for f(x) = cos(x), [-; 3'3 ] over this…

A: f(x)= cosx  , [ -π3,π3]as per MVT for Integrals for a function f(x) bounded and integrable on [a,b],…

Q: 2. Integrating factors found by inspection.: y(x² – y² +1)dx– x(x² – y² – 1)dy = 0 %3D

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Q: dx Evaluate the integral improper integral (2x – 1)3 00 A) 1/6 B) 1/8 1/4 (D) 1/9

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Q: 2- find an equation for the line through P and perpendicular to L and find the distance from P to L…

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Q: The general solution for the homogeneous differential equation y(5) – 2y(4) + 2y - 4y" +y - 2y = 0…

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