Consider the following. u = (-3, 3, 5) v = (0, 1, 6) Find u x v. Determine if u x v is orthogonal to both u and v by finding the values below. u. (ux v) = v. (ux v) = Ou x v is orthogonal to both u and v. Ou x v is not orthogonal to both u and v.

Q: Find the volume of the solid bounded above by f(x,y) = 8x², below by the xy-plane and the sides by y…

A: Volume

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1. lim 1+1/3 x-12x²+x-1

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Q: (A) = and B D = . Find the vector projection of A onto 2AD- BO O O O none of the above

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Q: For the function f(x) given below, evaluate lim f(x) and lim f(x). X18 8118 -x³ + x f(x) = √4x6 - 3…

A: We can solve this as follows:

Q: 7 4x + 10 Let f(x) This function has: 1) A horizontal asymptote at y = 2) A vertical asymptote at x…

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Q: Calculateri(t) r2(t)] and r₁(t) x r2(t)] first by differentiating dt the product directly and then…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 3t³i + 6tj - t²k (a) r(t) (b) r"(t) (c)…

A: Given data÷

Q: Solve the following differential equations of -x 2y" - 2y + y = 2e¯*

A: If the roots of the auxiliary equation are complex α±iβ , then the complementary function is…

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A:

Q: dw a) Find for the following function. dt w = 2ye* -In(z), x = ln(t2 + 1), y = cos(2t + 2), z = et…

A: If w=f(x,y,z) and x =g(t),y=h(t) , z=u(t) then,    dwdt =∂w∂x.dxdt+∂w∂y.dydt+∂w∂z.dzdt. Note : As…

Q: Find the volume generated by revolving the given bounded plane area about the line. Use shell…

A: Volume

Q: The equation 2k² - 3k 10 = 0 has solutions of the form k N± √D M (A) Solve this equation and find…

A: The given equation,    2k2-3k-10=0

Q: Use r = 6cos(7 θ) and r = 6

A: r1 = 6                                              1r2 = 6cos7θ      θ ∈0,π…

Q: Consider the parabola given by the equation: Find the following for this parabola: A) The vertex is…

A: The given equation,    fx=-9x2-18x-7

Q: Find E (p) for the price demand equation and interpret the results. x = f(p) = 1200(50p) where p-$28…

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Q: Question 2 Consider the equation: 2²-11-12 A) First, use the "completing the square" process to…

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Q: (A) = and B D = . Find the vector projection of A onto 2A - BO O O O none of the above

A:

Q: Let (A) = and B = . Find the angle between B and A D O [cos) 2/√(30(21)) O [cos] ^(-1) 2/√(30(21)) O…

A:

Q: II. Find dz Do not simplify your answers. 1. log,(√2x² + y) + tan(x − ³) = sin¹(x² - 1) +

A: We can solve this as follows:

Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept:…

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Q: 62. du * |x|dx

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim x-3 (x-3) tan(9-x²)…

A: As L'Hospital's rule is not to use so I have used the expansion of sin and tan function and easily…

Q: Find all real solutions of the equation 8m² -18-374. Write your answers as a list, using a comma to…

A: A detailed solution is given below

Q: 6. y" - 4y' + 5y = 4e³t; y(0) = 2, y'(0) = 7

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=8, and x=0 about…

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Q: d d Calculateri(t) r2(t)] and 77[r1(t) × r²(t)] first by differentiating the product directly and…

A: We need to find derivative.

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A:

Q: IV. Do as indicated. 1. Let f(x) = where = 1. 1 Find the equation of the tangent line to the graph…

A: Let's find.

Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Given point(1,-2,3) Then the equation of the line passing through 1,-2,3 is…

Q: [₁x³√x² + 3dx x-3 2

A:

Q: 5-10 Find the area under the curve y = f(x) over the stated interval. 5. f(x) = x³; [2, 3] 7. f(x) =…

A: Area

Q: Question 7 Consider the Quadratic function f(x) = 9x² 4. Its vertex is ( Its largest z-intercept is…

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Q: orrect. a k(t) ||r' (t) × r"(t)|| ||r' (t)||³ = r(t) = e¹0ti + e-tj tc

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Q: Y 4- y = f'(x) 3 -3 -1 (1,0) 2 3 -4 (-3,0) W (0,-0.5) (2,-0.5) (3,-2) -1,-2) -3- (-1,-3) (4, -3) 2 I

A: Observe the graph and answer the question.  Concept:  h'(x) = 0  : h(x) has local maxima Or minima…

Q: 4. Evaluate the following sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x)cos(2x) 12 sin(2x) sin(2x)…

A: Solution: ∫sinxcos2xsin3xdx

Q: (D² — 4)y = 8e²x — 12 - -

A: Given; D2-4y=8e2x-12 So, the auxiliary equation is; m2-4=0

Q: rπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

A: To evaluate the given definite integral.

Q: Evaluate the following limit using L'Hospital's rule. lim (e⁹x x⇒0+ 6x) ( ) +

A: Using LHospital Rule , limit is evaluated.

Q: Given : A B Ⓒ E b 27π²-24 [x³sin(2x) dx = . 64 2π 3 3π 4 TU 4 =|m 5 T 6 Find b if Isb -SOST

A:

Q: 27 If (2x 3) [133] [3] 3] -3 23 1. 2 13 2 2 3. 13 2 23 2 - 0, then the value of x is

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Q: 2b. Explain the difference between a partial derivative and a directional derivative.

A: Dear learner, as per our guidelines we can provide the solution for one part only. Kindly post other…

Q: Describe the long run behavior of f(t) = As too, f(t) → ? v As t→→∞o, f(t)→→ ? - 4tº + 2t6-3t5+1

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Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: 4. Evaluate the following sin(x)cos(2x)sin(3x) dx A. B. C. D. sin(3x) cos(3x) sin(2x) cos(2x)…

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Q: +x+1 2x² +2+x³+x dx = [Aƒ'(x) − B ln(g(x)] + D, and if A=B<0, then f x+2 -2x + +5In(x + 2) + C 2 x²…

A: Solution of the problem as follows

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: Find the slope of the normal line to the graph of g(x) = = at the point where x = 0. sin¯¹(x)+e²

A: Slope of the Normal line to the curve f(x) is -1f'(x).

Q: - 19 f(x+1)-(x2 - 6x +13) Ax + B √x²+bx+c² dx? (3)-In/x² - 6x + 13| + C The integral What is the…

A: Using partial fraction…

Q: Given: (1 + 2x) e-x dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the…

A:

Q: Question 4 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of ax²+bx+c²…

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