Find the value of § cot³(x) cosec“ (x).

Q: 14. Which of the situations below could – 100(+7)? A plane, currently flying at an alti A plane,…

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Q: /9-y dy

A: We have to integrate.

Q: Determine whether the following equality is true or false. 2-x2 D -1 x where D = {(x,y)| xr² + y²…

A: ∫∫Df(x,y) dA = ∫x1x2∫y1y2 f(x,y) dy dx.

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Here, note that any plane through the point P(14,-12,7) is of the form:…

Q: ecot x 20. J sin² x(e- cotx) ax is equal to A. ecot x 1 + C ecot x C. -ecot x + C D. –ecot x + C

A: Given problem:-

Q: S (x² – 12x + 100)(6 – x)dx -

A: We can solve as follows

Q: Use the method of reduction of order to find a second solution of the differential equation 1?y" +…

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Q: Given the plane i = (-2, 1,5) + s(3, -2,0) + t(1, 1, 5), s,t € R. The plane cuts the x, y and z-axes…

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Q: 11) The Inverse of ()= *-1* a)(x) 3x-1 b)/(x) log2(x) d)f(x)= log3(Vx+1) e) non

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Consider the following. u = 5i + 4j, v = 31 + 2j (a) Find the projection of u onto v. 33 3i + 2j 13…

A: u = 5i +4j v= 3i+2j   a projection of u onto v  = (u*v)v/|v|2 u*v = 15 +8 =23 |v|2 = (32+22)2 = 13…

Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 au. (v x w)| to determine…

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Q: Evaluate the indefinite integral. x° (x® + 1)1/2 dæ Integral = INOTE: Remember to enter all…

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Q: Evaluate the indefinite integral.

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Q: 1 (5* )csch dy x+1 1. (а) if Find dx x > 0. y = (ecosh S* ) In(Vx² +1

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Q: Question 2 of 10 View Policies Current Attempt in Progress Find the directional derivative of f at…

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Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

A: Solution: Let u = ai+bj makes an angle of 45 degree with v = 9i +4j

Q: Find an equation of the tangent line and normal line to the curve given by f(x) = x? – 6x + 5 at the…

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Q: 1 (5* )csch- if y= (e oshS ) In Vx² +1 2 a) Find dx dy x+1 x>0. 2 x++1

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Q: Determine whether the lines Lj and L, are parallel. Lj: х%3D 3 — 31, у %3D 5 + 1, L: х%3D6 — 9t, у…

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Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z =-13. Find the following. 1. The cosine of the…

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Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Scalar Projection of AP on AB is defined as AP→.AB→AB→

Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: (0 if –2…

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Q: Consider the following functions. f1(x) = 3 + x, f2(x) = x, f3(x) = x2 g(x) = c,f,(x) + czf2(x) +…

A: Let's find.

Q: Jse vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (-5,…

A: Suppose, A(1,1,3), B(-5,5,0), C(-3,8,-7) & D(3,4,-4) are the given vectors.

Q: Find the area of the triangle with vertices P(1, 2, –3), Q(0,0,0) and R(3,4, 1). NOTE: Enter the…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z² (2,…

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Q: (5) Radioactive decay is measured in terms of "half-life", which is the number of years required for…

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Q: Find the area of the parallelogram that has u = 2i – j+ 2k and v = 2j + 3k as adjacent sides. %3D…

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Q: Find the area bounded by these curves. (All choices are in sq. units) y1 =+4 Y2 = r-2x

A: This question is related to application of definite integration, we will solve it using given…

Q: dy +y= y2 sin x

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 12у — 9г — 3 %3D 0 (a)…

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Q: Perpendicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Solution of question is written in below steps.

Q: Given that Vf(11, –6) = 10i – 8j, find the directional derivative of the function f at the point…

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Q: Find the directional derivative of f at P in the direction of a. f(x, y, 2) = xy + 2²; P(2,-5, –1);…

A: Given query is to find the direction derivative. BB

Q: Consider the points A(3, –3, 2), B(4,–5,0), C(-1, –4,0), and D(6, 2, –3). (a) Find the volume of the…

A: AB→ = i -2j-2kAC→ = -4i-j-2kAD→ = 3i+5j-5k Volume of parallelepiped with AB→, AC→ ,AD→ as adjacent…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Find the radius and interval of convergence for the series (n!)2 (2n)! (æ – 5)³n - n=1

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Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A: Given

Q: Fin d: ) (3x*arctan x do Evaluate: s.) dx

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Q: Instructions: (I) Use Limit Laws to find the limit of each given problem. (II) You may only use…

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Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: Find Duf at P. f(x, y) = sin(4x – 2y); P(2,4); u = i j - NOTE: Enter the exact answer. Duf :

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Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 6, 11), and (1,0,-1).…

A: Given

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 4 V3 and whose components have…

A: Given:     Let v=x,y,z be a vector in R3 with length v=43 This is x2+y2+z2=43            x2+y2+z2=48…