Find T,N and k for the curve: 1- r(t) = (6 sin 2t)i + (6 cos2t) j+5tk.

Q: sv x² + 2x dx

A:

Q: In spherical coordinates, the equation below describes what? O a plane O a cone O a sphere O a…

A: topic- spherical coordinate system

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =…

A: Here, the given vector field is: F=x2i+5xj+z2k⇒curl F=ijk∂∂x∂∂y∂∂zx25xz2…

Q: Find the ratio of the length of minor axis to the length of the major axis of the ellipse 9x2 + 16y2…

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Given

Q: E = 5 -2 -4 3 2 2 -4 -4 -4 0 -3 2 3 2 4 4 -2

A:

Q: On the Illinois state tax form, numbers are to be rounded to the nearest dollar. If Heat earned…

A: If you have to round off to complete integer then we need to look the first number after decimal.

Q: 1. I. Evaluate each determinant. -5 -3 3 -4

A: Given,            -5-33-4

Q: Evaluate 0-2²-²4 where is a unit cele centered at the origin

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Q: Suppose a state's income tax code states that tax liability is 18% on the first $19,500 of taxable…

A: The tax function,   T(x)=a+0.18xx≤19,500b+0.14x-19,500x>19,500

Q: the Following differential equation ²²=1+ P²

A:

Q: Given the definite integral, its limits are to be substituted to x³ dx x + 1 x² x² 2 x3 3 Option 1 +…

A: Given problem:-

Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

A:

Q: A gas station sells Q gallons of gasoline per year, which is delivered N times per year in equal…

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Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A:

Q: Calculate the gradient of h(x, y, z) = x z Vh=

A:

Q: The integral represents which quantity? O the total mass with density F O the length of the curve C…

A: Solution

Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

A:

Q: 6. I. Evaluate each determinant. тут 3-3 4 1 -5 0 -1 -4

A:

Q: 100 (e) Σ199 2i(i3 – 1) i=1

A:

Q: Given f(x) = x-1 2 on [- 2, 2]. x²+1 a. Find the critical numbers of f on the given interval. b.…

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Q: b). Using an appropriate triple integral, evaluate the volume of: [Verify using Mathematica 1). ii).…

A: We have to find the volume.

Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

Q: Question 9 This triple integral represents the volume of a cylinder. O True O False V = f²" f² fr dz…

A:

Q: Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 5π/4…

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Q: Find the average value of the function on the given interval. f(x)=√√x+3; [1, 13] (Type an integer…

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Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

A:

Q: Assume A = 21 2] and B = 1 3 [43] [4 3 11 7 6 show that (AB)' = B' A'

A: Given matrices A and B, To show that AB'=B'A'

Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

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Q: Find derivative A) y=sin x/1-cos x B) p(x)= 3/1+10e^4x Simplify answer

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Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: Evaluate the following integral. JIS x ln y tan z dV if S = = (x, y, z) € R³ : −1 ≤ x ≤ 0, e ≤ y ≤…

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

Q: 13. In |z|

A: It is depend upon the property of complex number and thier Logarithmic.

Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-

Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: I. 7. Evaluate each determinant. -3 4 -5 2 -3 -5 1 5 3

A:

Q: If u = 0 (and neither of them are zero vectors), then the two vectors are orthogonal (perpendicular)…

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Q: P 2. ( Use the disk or washer method to find the volume of the solid obtained by rotating the region…

A:

Q: First the pieces: End result (in terms of just t): dt 江 西 | Use the chain rule to find where 11 z =…

A: if z is function of x and y. Also x and y are of function t then derivative of z w.r.t "t"  is…

Q: √ √(x²-1)dx

A:

Q: Question 8 f the Cartesian coordinates of a point P are (0, 1, 1), then the cylindrical coordinates…

A: Convert Cartesian coordinate to cylinderical coordinates

Q: Suppose parametric equations for the line segment between (-2,-5) and (0, - 5) have the form: [ r(t)…

A:

Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

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Q: Set up the integrals (No need to compute) for the volumes of solids of revolution by revolving the…

A: Given

Q: Convert the Cartesian coordinate (-1,-4) to polar coordinates, 0≤ 0 0 Enter exact value. 0-

A: Given, (x,y)=(-1,-4)

Q: Use finite difference approximation to find the values of y(0.25), y(0.5), and y (0.75) for the…

A: