P2: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x - 3y - 2 = 0 is revolved about: A. x-axis. B. y-axis.

Q: Given the graphs determine the integral to find the volume, if it is rotated about the x- axis (1,…

A: We have to find the volume.

Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost…

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Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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Q: d. State the equation of the vertical asymptote of f(x)=log, (x+1). e. Sketch a graph of f(x) = log,…

A: We have to find the asymptote of function and graph

Q: Set up the definite integral required to find the area of the region between the graph of y= 2²-12…

A: find intersection point

Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and calculation we will…

Q: 5 -5 g(x) dx

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Q: z (hx) = h + k

A: y'+y=(xy)2

Q: Write the given statement into the integral format. Find the total distance if the velocity v of an…

A: The velocity of an object v=t2-3t+2 m/sec. over the time period 0≤t≤2

Q: S # 3 X Use the fundamental Identities to simply the expression. 1) tan & coft 2) cos²0 2 +CSCO sint…

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Q: [44 408]. -4 -18 Find the eigenvalues and eigenvectors for A = [64 The eigenvalue a + bi = has an…

A: Using Matrix operation

Q: A sketch of the region enclosed by y = x and y = f Area of the region = fot 4.25 2²+1 follows.

A: Given: y=x and y=4.25xx2+1 First find the intersection point Thus, x= 4.25x1+x2 ⇒1+x2= 4.25⇒x=…

Q: any decimals to the hundredth place. f(x) = -log(x + 50) + 2 x- intercept: (50,0) y-intercept:…

A: Explanation of the answer is as follows

Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, cos x = 0, y() = 0…

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Q: 8. 9. 10. Given f(x) = cos(3x + π), find ƒ'(π) a) 0 b) -1 c) -3 If f(x) = √ex, the derivative is: a)…

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Q: (13+3^3)/4+4/2*6/12 020 011 030 ONone of the above

A: In this question, we will use order of operations.

Q: Given f(x) = sech (x) and below is the graph. Determine the domain and range for f(x). f -1 ii)…

A: Pu

Q: 36. If cos(30+y)-- A) B) which would be sin(30-y)? C) pr D)

A: Topic:- trigonometry Note:- as per our guideline if more than one question uploaded than only first…

Q: Vector A) Prove that: Vx (FxG) = (GV)F- (FV)G+ F(VG) - G(VF). 201 1

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Q: 2. Find the Maclaurin series of f(x) = tanh

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

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Q: Find the one-sided limits of f(x). Step 1 of 2: Find lim f(x). x--7 f(x) = -7x-3 -4x² + 4 if x < -7…

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Q: find differential equation of the following equation 1) y' = -x y+x

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Q: EXAMPLE 1(DISK METHOD) Find the volume of the solid generated by revolving about the x-axis,the…

A: Given problem:- EXAMPLE 1(DISK METHOD)   Find the volume of the solid generated by revolving about…

Q: Find the general antiderivative of f (x) = O2 ln ln 2x + C 1 O + C - 2 ln 2x O-In In 2x + C 1 O + C…

A: The function is given by fx = 4xlnx2 To evaluate: The most general antiderivative of the function.

Q: Use definition of derivative to find derivative of the function f(x)=3/x+2, at x=-1

A: Given f(x)=3x+2    at x=-1To find f'(x) at x=-1

Q: If a parabola's focus is at (-2,5) and directrix is at y = -1, what is the vertex form of the…

A: The correct answer is option (2).

Q: 5. Find the volume of the solid in the first octant bounded by the two cylinders x²+y²=4 and…

A: I am attaching image so that you understand each and every step.

Q: A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying…

A: I am attaching image so that you understand each and every step.

Q: Evaluate the spherical coordinate integral. 1- cos 2 2π π SS S p²sin & dp do de 00 0

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Q: Find the transition points. y = 3x² - 42x6 (Use symbolic notation and fractions where needed. Give…

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Q: Evaluate the following integrals: dx dx ·S b. S √81+16x² √16x²-9 a. dx 49-4x² c. S.

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Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and concept we will…

Q: Differentiate and simplify this function f (x) = x^2/3 sin(x)

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Q: Determine whether the improper integral is convergent or divergent. 33) S ∞ dx x2/5 0 A) Convergent…

A: We know that integration of xn   is xn+1/n+1.   Here i attached the solution of this question.

Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

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Q: ● -5 13 10 5 Enable Zoom/Pan x -10 10 5 Keyboard cting a radio button will replace the entered…

A: We will solve the limit.

Q: Find the average value of f(x) cos¹ sin x on the interval [0, 3]. = Answer: 3-cos(1)/5

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Q: Sketch the region enclosed by y = 3x and y = 52. Find the area of the region.

A: Given that y=3x and y=5x2 find bounded area.     Here i attached the solution of this question.

Q: The shaded region between the graphs of y=-22² +20 and y = 3x - 15 is displayed below in orange. -40…

A: Area of a region is given by ∬dydx, when the rectangle is choosen parallel to y-axis.Area of…

Q: Evaluate the following integrals: 1. f (cosx- sin x) dx 2. fcot²x dx 3. f (sin x + x) dx

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Q: What is the subtraction of Vector M from Vector T? M = 5 units T= 4 units

A: Solved below

Q: Set up the definite integral required to find the area of the region between the graph of y = 12-2²…

A: we have to find out area

Q: Evaluate the integral In 23 In y s s ex+y dx dy.

A: Given: ∫1ln23∫0lnyex+ydxdy

Q: Evaluate the integral f [[ - Y sin(x²)dxdy.

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Q: Find the general antiderivative of f (x) = 4 x ln x²

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Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

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Q: Evaluate the integral. π/4 Jo 0 sin5(x) dx

A: Given query is to find the value of the integral.

Q: Determine the equation of the hyperbola with center (-1, −6), a focus at (−1, −16), and a co-vertex…

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Q: A tank in the shape of an inverted right circular cone has height 7 meters and radius 2 meters. It…

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