Find the area of the surface generated when the given curve is revolved about the given axis. y = 3x + 5, for 0≤x≤6; about the x-axis The surface area is square units. (Type an exact answer in terms of t.)

Q: calculate the derivative below using the definition of derivative. f(x)=e^[cos(x)]  a = pi/2

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Q: x² + y² = 7 X=7 O igular (solve) x² + y² = 49. - Option 1 O

A: Given that r=7  r2 =49 let x= 7 cos(theta) y=7 sin(theta)

Q: Convert the rectangular coordinates to polar form (√8,√8) (solve) (4,5) (4,5) Option 3 O (√2,75)…

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Q: 3. Let f(x, y) = x³ 3x² + xy +7 and u = 0.6i + 0.8j, then find Duf(1,-2).

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Q: b = 2i + j + 3k 14 direction of a = Select one: O True O False is the unit vector in the 2i + j + 3k

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Q: The symmetric equation of the line that passes by P(1, -1, 1) and Q(3, 2, -1) is: Select one: x-1 0…

A: This question can be solved using the concept of lines in three dimensional geometry.

Q: Find the limit. (HINT: Treat the expression as a fraction whose denominator is 1 and rationalize the…

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Q: Increasing global temperatures raise sea levels by thermal expansion and the melting of polar ice.…

A: Given L(x)=0.02x3-0.07x2+8x where x is the number of decades since 2000.

Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to analyze and sketch a graph of the function and find any intercepts, relative extrema,…

Q: Find the distance from the point (-4,3,-2) to the yz-plane.

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Q: The definite integral is equal to O 2 [²x Select one: 4 O f₁²₁x² dx + ₁ + x² dx none of the others ○…

A: ∫02 x2dx here we have to find equal to this. split the integral into two  use formula  ∫a  b f(x)dx…

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: The definite integral is equal to Select one: none of the others 02 -16 [²(3x² + 4x³)dx O-8 0-6…

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Q: The distance from the point K(3, -2, 0) to the az- plane is Select one: O-2 O √13 O 0 02 O None of…

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Q: a. Find an equation for the secant line through the points where x has the given values. p. Find an…

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Q: [1 Q6: Find A1 where A = 3 2 -1 6 1 0 -2 4

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Q: Find dy if the curve is described by the equation x³ 4x³y + 3y² +Ske y

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Q: Consider the triple integral of f(x,y,z)=(z²)(x²+y²+z²)¹/² over the solid region S where z is…

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Q: The number of people in a town of 65,000 who have heard an important news bulletin within t hours of…

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Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

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Q: The value of the definite integral 3 [² (3x² Jo 0 is (3x² - 2x + 4)dx

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Q: Sketch a graph of the function f(x) = 3 cos 6 5 4 3 2 1 -8п -7п -бп -5п -4п -3л -2л -π -1 -2 -3 -4…

A: This question is based on graphing a function from its principal function.

Q: 100 100 suppose that Σ a; = -17 and Σ b; = 13. compute the sum. i=1 i=1 100 Σ ( – 30a; – 76;) i=1

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Q: Determine the Riemann sum using L4 over the interval [-1,1]. y = 3x² - 2x + 1

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Q: Given the values of f(x), g(x), f'(x) and g'(x) in the table, answer the following questions. x f(x)…

A: We can find the answer using the data given in the table as below.

Q: Find the derivative of the function. f(x) = ex In(x³) f'(x) = X

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Q: A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 3x. The…

A: We need to find height.

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: For the following function f, find the antiderivative F that satisfies the given condition f(v) =…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: Integrate the integrand (x2-x+12)/(x3+2x) .

Q: a.) S (t² – 9) (4 – t²) dt from 2 to 3 b.) fx dx from 1 to 2 c.) f (x² - d.) f sin 0 de from 0 to…

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Q: 1 2 1 Q2. If A = 200 31 2 find A¹.

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Q: Congratulations! You won a contest sponsored by a local radio station. If you were given the choice…

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Q: The intervals on which f(x) = x² In x is increasing and decreasing, and the intervals of concavity…

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Q: Consider the following graph on the interval - 360° < x < 45°: 360 -330-300 270-240 -210 -180 -150…

A: We have given a graph of function. And find to amplitude, period and function

Q: The Taylor series expansion of 2 |z| < 1 is (solve) Z-2¹ −(¹ + ² + ² + ² …..) X Option 2 O…

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Q: Q2: Fill in the blanks : 1- ff f(x,y)dydx represents the. 2- y" +(3y')5 - sinx = 4 of order 3-ye…

A: Since multiple questions are asked I am answering first 3 subparts

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0, 4, — 3), and R= (-6, -1, - 5)

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Q: se series to evaluate the limit. 2 lim h→0 (sin h)/h- cos h h²

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Q: Consider a solid G, generated by rotating the region bounded by y = 2x² and y = 0 from would the…

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Q: f(t) = sin(wt) u(t) Do the laplace transformation of the math in details.

A: we have F(t) =sin(ωt) u(t)

Q: Juan Dela Cruz wants to deposit ₱5,000 every quarter at 16% compounded quarterly for 5 years. How…

A: We have to find out solution

Q: B: e²+² dydx Jo Jo

A: To solve the integral ∫0∞ ∫0∞ ex2+y2dydx

Q: If v=3i+2j+ k,w=3i+ 4k and the angle between v and w is 90, find v.w (solve) 10 8 0 O Option 3 O

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Q: approximation with 5 subdivisions. 3 2 1 2 3 4 5 6 7 P∞ot 8

A: solution is given below

Q: 3x 2. y = Ae³x cos x+Be³x sinx

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Q: Convert the rectangular equation to polar form x² + y² = 9 (solve) rsino = 9 r=4.5 Option 4 O r=3 r²…

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Q: Write an equation for the transformed logarithm shown below, that passes through (2,0) and (1,3) N 4…

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Q: Q1) Find the derivative a) f(x) = arctan (e-2x) b) f(x) = [arcsin (2²)]³ C) f(x) = tan (lnx) + 52²

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