Find the vector equation that represents the curve of intersection of the paraboloid z = surface x = e². Write the equation so that one of the functions is simply t. x(t) y(t) z(t) = = = = 3x² + y² and the

Q: Find the exact area of the surface x = 6t - 2t³, y = 6t², obtained by rotating the given curve about…

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Q: 32. The radius of a circle is increasing at a constant rate of meters per second. What is the rate…

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Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: Find a polar equation for the curve represented by the given Cartesian equation. x² + y² = 4cx k

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Q: 1. (6413 #4 p. 351) The cross section of a large tank is a trapezoid. The short side of the…

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Q: * Your answer is incorrect. Consider each function to be in the form y = k xP, and identify k or p…

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Q: Find the mass of the lamina bounded by the graphs of y = x² and y = x with mass density p(x, y) = x

A: As we know the expression for the mass of the lamina body is: m=∫cd∫abρx,ydydx   The given curves…

Q: Given the non-homogeneous differential equation y "- 4y + 4y=e²x What is its auxiliary equation? 0…

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Q: 12) y = 2-X; dy 3x+1 A) -7 (3x+1) dy = ? ² B) 6X-5 (3XH) 2 c) (3x+1) D) = ¹ 3+2X

A: NOTE: Refresh your page if you can't see any equations. . take derivagive

Q: At time t, the position of a body moving along the s-axis is s = t³ - 9t² +24t m. a. Find the body's…

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Q: Suppose a real number t determines the terminal point (a, b) on the unit circle as shown. (a,b) ▶ D…

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Q: Obtain the general solution of the D.E. y - 4y + 4y=e²x O 1 + y=c₂e²+ = x²e² O 1 2x y=₁₁²³² +₂²² + =…

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Q: Match the following functions with the general shape of their graphs. Functions f(x) = ln (x + 2) -…

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Q: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

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Q: Find a Cartesian equation for the curve and identify it. cos(20) = 1 O limaçon Ohyperbola O circle O…

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Q: a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 13…

A: We will find the required.

Q: ind the equation of the plane that contains (1, -2, 1), (1, 0, 2) and (0, -2, 2)

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Q: (a) nsider the change of variable from cartesian coordinates (x, y, z) to coordi- nates (r, y, 0) in…

A: Please see the below pictures for detailed solution.

Q: Find the exact length of the curve. x = e² + e-t,_ y = 5 - 2t, 0 ≤t≤ 2

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. rsin 0=6 The…

A: in cartesian  coordinates  x=rcosθ  and  y=rsinθgiven  rsinθ=6

Q: Evaluate the integral by making the given substitution. sec(52)tan (5x)dz, u = 5x + C

A: we know that   dxndx=nxn-1d(secx)dx=secxtanx

Q: Consider the following functions. f(x) = x², g(x)=√x-7 Find (fog)(x).

A: Given,            fx=x2 , gx=x-7

Q: Sketch the curve. r = 9 cos(8) O -4 ac -2 O y 2 -8…

A: Given query is to sketch the curve and find the area.

Q: Let y(t) be the solution to Use Euler's Method with time step ntn 00 10.2 20.4 30.6 40.8 51.0 Yn 2…

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Q: 6. f(x) 10. f(x) 12. j(x) f(x) 14. 16: Function 3. 7. 9. 11. f(x) 13. f(x) 15. f(x) 17: f(x) 15.…

A: Match the function with the graph of its derivatives.

Q: Find the area of the given region. Use a graphing utility to verify your result. y = 1 + In x³ X y 1…

A: We can find the area of the region .

Q: 1. Given the equation y = -7cos(4x + 20), find the following: (write the answers here and on paper)…

A: To solve the following problem and find the following things

Q: Use reference angles to evaluate sec Enter the exact answers. For the number 7, either choose from…

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

Q: Find the limit of f(x) = lim f(x)= -7+- X as x approaches co and as x approaches -8. lim f(x) = X→∞0…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: The cost function for a particular product is given by Cx) - 0.0001x³ +0.018x² +26.7x + 190 dollars,…

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Q: If f(x)= f'(x) = = tan z sec x -4

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Q: 12. Find f x √(1-x²)³ dx

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Q: Find the length of the spiral r=0², 0≤0≤ √21. The length of the spiral is (Simplify your answer.)

A: Topic = Integration

Q: f(x) = x4−32x−12  Determine where the function is concave up and concave down. Enter your answers…

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Q: Which of the following represents a geometric sequence with a common ratio r = 5?  1 2, 10, 15, 75,…

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Q: Let C be a cylinder of radius 5 whose axis of rotation is the y-axis. Draw a graph of C and then…

A: We need to find equation of cylinder. As per Bartleby guidelines we can solve one question from…

Q: 17. f(t) is the graph shown below and g(x) = f f(t)dt. Find g(0), g(1) and g(4). D 2 3

A: Let's find value of g(0),g(1) and g(4).

Q: Find the derivative of: 7 sin² ( – 2xº).

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: Determine the solution of the following differential equations. c) (D¹ + 2D6 + 7D5 + 14D4 + 8D³ +…

A: To determine the solution of the following differential equation.D7+2D6+7D5+14D4+8D3+16D3-16D-32y=0…

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

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Q: Evaluate the integral by making the appropriate substitution: u = f2¹ (25 - 4) 43³dz = dx 43 fz¹ª…

A: To evaluate the integral.

Q: Vectors are shown in the graph. n Or O q Ou 7 n 60 5 3 2 1 T -2 P XX u S ? 1 2 3 Which of the…

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Q: Suppose g(x) has a range of [-2, 6]. Determine the range of the transformation y = 2g(x) - 5 O [-14,…

A: Given: Range of g(x) is [-2,6]

Q: On the interval shown, for which graph is f' positive and f"' negative? OA. OB. Q O C. z Q 2 OD.

A: To choose the graph which describes the given characteristics

Q: Let f(x) 0 = c-8 Oc==3 Oc=2/20 Oc-4/ 11 2xc + 1 C + 3x 3 ▸ Determine the value of c so that x = 9 is…

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Q: Given the non-homogeneous differential equation y "+ 3y + 2y = 4e* The roots of its auxiliary…

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Q: Find two points where the curve x² + 2xy + y² = 53 crosses the x-axis. The tangents to the curve at…

A: We need to determine slope.