Find the Volume: Rotate the region bounded by x = y²-6y + 10 and x = 5 about the y-axis

Q: 10. f cos*x sin x dx 11. (sec² 3x) dx / (tan 3x) 12. Setan 2x sec² 2x dx

A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

Q: Suppose f(x) = 3x² + x - 3x²+x-6. Compute the following: A.) ƒ( − 4) + ƒ(1) = = B.) f(-4)-f(1) =

A: Given f(x)=3x2+x-6f(-4)=3(-4)2+(-4)-6=3(16)-4-6=48-10∴f(-4)=38

Q: (b) Find d'y dx² where x + 2y = 1.

A: In this question, we want to differentiate the given expression two times.

Q: Determine the critical point/s of f(x) = ln(x2 + 4x + 14) on [-4, 2]. ΟΧ -- -2 Οχ -3

A: Given, f(x)=ln(x2+4x+14) on [-4,2]

Q: Determine

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Q: 1) a) Find all vectors such that X = b) Explain why there is no such that X =

A: Solution: a) let v = (a, b, c). Then

Q: The angle between the vectors [√2 – 1, √2 + 1, √2] and [1, 1, 1] is: 45° 60° 90° 30°

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Q: Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-y' + (x² - 1) y=0, x=…

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Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

Q: cos(etan 3x) y cos

A: The given function y=cosetan3x

Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

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Q: 5. Two planes are perpendicular if their nommals: a) have a cross product of zero c) have a dot…

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Q: find The angle of the triangle whose vertices are C(1,-2, 2) Points AC-1,0,2) B (2,1,1) A B

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Q: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

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Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation

Q: Consider the function f(t) = = -X 3-x (x − 3)² - if x 3

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Q: (2) Consider the function where a, b are constants. g(t) = if t 1

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Q: Solve the integral shown below. . S | xsin xdx

A: Given problem:- ∫x sin(x)dx

Q: dy For the following composite function, find an inner function u = g(x) and an outer function y = f…

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Q: 20. Stan² x dx

A: Consider the integral  ∫tan2x dx

Q: The integrating factor of the differential equation A. cos x B. secx +y tanx - secx = 0 i= C. ecosx…

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Q: Vectors [2, 5, a] and [-6, b, 9] are collinear. What is the value of ? a a) 5 b) -3 Oc) -5 d) 3

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Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: (5x-5)dx 3x² - 8x - 3

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Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A: This is  a problem related to maxima and minima of the function. Based on the general formula and…

Q: a. g(3) = = b. lim g(z) C. lim g(z) d. lim g(z) = Z-1 = -4 -3 -2 -1 10 6 2 0 -2 -4 -6 9(z) 2 3 5 6

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Q: Question 4 (a) Solve the following: [²4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: √√3 L dx 1+x²

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Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: Pls help ASAP

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Q: ל 15 18 a = (3₂16) 6= (-2,0,1) → 08 -> 2² = ²²-23 +5k →> oc CẢ OA

A: Given :a→=3,1,6=OA→b→=-2,0,1=OB→c→=i-2j+5k=1,-2,5=OC→

Q: f(x csc² 2x - x cos x cos 2x)dx

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Q: 4.1 Evaluate the integral [3√x √(3√x - 1 / +5 4 + x² expressions after applying the integration…

A: We have to evaluate the integral

Q: Evaluate In x x (4 - In² x) - In 14- In² x | +C - 2 In 14-In² x | +C 12 -dx In | x (4- In²x) | +C In…

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Q: Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: let  x, y, z  be the non zero  vector that is orthogonal to   u, v and w

Q: If z is a variable, then the infinite series of the form is called n Σ" =a + a₁ + ª₂x² + ... + ª₂x”…

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Q: Find the area of the surface that results when y= around the x-axis from x = 1 to x = 2 223 is…

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Q: Complete the parametric equations of the line through the points (7,3,-5) and (0,6,1) x(t) = 7 - 7t…

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Q: Q15) Given that y₁ (t) a) t b) t 21 31 41 51 = t¹ is solution for 2t²y" +ty' - 3y = 0,t> 0, then y₂…

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Q: 9) Ур H Asin(2t) + Bcos (2t) Q13) The general solution for y' a) = 3x² + c b) = y Q14) The solution…

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Q: Q1/ Solve partial differential equations д2u 1- =+2 Әхду Х

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Q: Given f(x,y)=x2y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

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Q: quickly

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Q: .) Find the limit or show that it does not exist. lim √25t²+2-5t 1-x

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Q: If dy dt y. 1 - et and y = 0 when t = 1 find

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Q: Let ā 47- 57 and b - 27 + 3j + 4k. Find - 2ā - 36.

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Q: Assume that the number of bacteria R(t) (in millions) present in a certain culture at time t (in…

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Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions, labeling…

A: The function satisfies the condition,The domain of fx is -∞,∞f'x=5x2x2-3f''x=10x2x2-3f0=0

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: x(t) = Find a plane containing the point (-3,5,-2) and the line y(t) = z(t) = 5 - 3t 8 + 6t 7 + 6t

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