Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form) that contains point P and line l.

Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √x, 1 ≤ y ≤2

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Q: A sphere has a diameter whose endpoints are Pi₁(3, 2, 1) and P₂(-1,-4,-4). Find the equation of the…

A: We will solve the problem

Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

A: topic- algebra

Q: C. Find the volume of the solid obtained by rotating the region bounded by y = -10 + 6x-x², x = 1…

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Q: Convert the Cartesian coordinate (-5,-3) to polar coordinates, 0≤ r = 0 = Il

A: We have to find polar form

Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. HI-4 (a) lim f(x)g(x) #114 (b) lim…

A: Given problem:-

Q: Given: parametric curve H defined by r(t) = tan-¹t and y(t) = eªt, where t = R (a) Find the slope of…

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Q: Using trigonometric substitution to solve x-2√4 – x²dx = f f (0)d0. What is (a − b + ²)? A B U D I…

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Q: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

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Q: THE AREA BOUNDED BY THE PARABOLA y² + x - 2y = 1, THE X-AXIS, AND THE REVOLVES ABOUT THE LINE LINE…

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Q: Given the following sets: U= (Kazoo, French Horn, Guitar, Ocarina, Bamboo Flute, Viola, Saxophone,…

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Q: In evaluating 5 dx =, is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=4.6.…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, −12t) (a) If R(0) = (-1,4,-5),…

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Q: What monthly compounding nominal interest rate is earned on an investment that doubles in 10 years?…

A: We have to find the interest rate.

Q: A product can be produced at a total cost of C'(x) = 500 + 100x2 + x³ dollars, where x is the number…

A: Given that; Cost function and revenue function.

Q: 4 3. 2 1 -4 -3 -2 -1 2 -1- -2- -3+ 3. From the above graph of y = f(x), find the following limits:…

A: a)2  b) -2  c) -4

Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with…

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Q: Let C be a curve with the parametric equations à = − ln(t + 1); y = sint, t = [0, 1]. a. Set-up the…

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Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: True or false If cosh x = then sinh x=

A: We have cheek the statement

Q: 9. y(y² + 1)dx + x(y²-1)dy = 0 Ans: + xy = c

A:

Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: ∫-22(x+1)(x2+2)2(x2-1) dx

Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin (2x - 6) sin(4x12)…

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Q: Find the intercepts and the vertical asymptote of x²-2x-3 4 Enter the intercepts as points. (a, b),…

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Q: Considering C is a curve which has the following parametric equations: 1 t³t+1, C = { x (t) = { 1³3…

A: Parametric equation

Q: The rational expression A TRUE B FALSE 1 (9x² +16)² can still be decomposed.

A: this can not be decomposed. This statement is false.

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: x6 cos(x³) A) True B) False |dx=0

A: We have to check by even or odd function

Q: What is the domain of each part of the piecewise-defined function? (Enter your answers using…

A: Given that fx=-1.95x+25.90.535x2-1.58x+6.2Solution :Intersection point of piecewise-defined function…

Q: Calculate the integral approximation S12 for Si ²1 dx. +1 S12 =

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Q: If S x²+x-2 (x2-1)(2x-x²) dx AS + Bf f(x) dx + D f g(x) dx, then x dx can be resolved into A ...

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. Round your…

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Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all x € (a,…

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Q: Find the area bounded by the parabola x = 8+2y-y², the y-axis, and the lines y = -1 and y = 3.

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Q: Find the area of the region bounded by the curves y=x4 andy=2x-x²

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Q: A bicycle with 20-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels…

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Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: projectile motion

Q: Find the volume generated by revolving about the y-axis the area bounded by y2= x-2, y=x-4 Use shell…

A: Here we have to find the volume by using shell method.

Q: A runner is jogging at a constant speed of 3.5 miles per hour. a. Find the distance d that the…

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Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

Q: Find the transition points. f(x) = = x(5 - x)¹/3 (Use symbolic notation and fractions where needed.…

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Q: For each system below that is linear, determine whether it is consistent. (a) 3x₁ - x4 = 1 3x₁ + 3x₂…

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Q: Find vertical asymptote, x intercept and y intercept of (x+1)(x-5)/(x-6)

A: Topic = Functions

Q: By method of Integration by Partial Fractions, A B(2x-2) + C (x³+5x²+6)dx (x²–2x+5)² = √ [₁²-2² +…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: 2 2 2 Find the moment of inertia: x3 + y3 = a3 about x = = 0.

A: Let's find moment of intertia.

Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: the following function problem: check that the is harmonic and determine it it is a harmonic…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: 18. What is the length of the polar curve below? 3πt x = 8cos (0) for 0 ≤ 0 ≤ ³1

A: