Find the distance from the point P(1, 2, −1) to the line passing through the points A(−2, −3, −5) and B(4, −3, −2).

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Q: A B C d Using integration by parts, Then k is? (a)-1.5136 5²x² ²x³ cos (x²) dx = k - S²x - [*x…

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A: We have to find the volume.

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: Find f. f(t) = 5e¹ - 6 sin(t) — 5 f"(t) = 5et + 6 sin t, f(0) = 0, f(π) = X 0

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Q: Find the area bounded by y³ = x² and x-axis, from x = 0 to x = 8.

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Q: Find the area bounded by the parabolas (x-2)²-9py = 0 and y² = 9p(x-2).

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Q: Jonathan invested $240,000 to purchase a home. After 14 years, he sold the home for $320,000.…

A: We have to find interest rate on the investment.

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Q: Find a particular solution of =(x−1)² if y=-21 when x=-3. dx

A: dydx  = ( x - 1 )2   , y = -21, x = -3 we have to find particular solution of it

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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: 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

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A: In this question, we want to know whether the given statement is true or false.

Q: Using Simpson's method x²dx for n=4 is equal to Blank 1 (use 2 decimal places with proper rounding…

A: SOLUTION-

Q: Evaluate the double integral that will find the volume of a solid bounded by z = 4 − x^2 − 4y^2 and…

A: Let's find volume of solid.

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Q: example of properties of definite integral

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Q: Solve • ƒ²₂(x + 1)(x + 2)²(x² - 1)dx with and without the even-odd theorems (show both solutions).

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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.

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

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Q: A payment of $2,600 was due three years ago, and a payment of $1,450 is due today. What single…

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Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Calculate the integral approximations To and M6 for 10 x³ dx. Your answers must be accurate to 8…

A: ∫ab f(x) dx≈Tn=∆x2fx0+2fx1+2f(x2)+...+2f(xn-1)+f(xn) ∫ab f(x) dx ≈Mn=∆xfx¯1+fx¯2+...+f(x¯n) ; where…

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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: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t == . — = dt

A: Given:ds/dt=10csc^2(2t) To find: solution at s=2 and t=π/4

Q: 1 Find the arclength of the curve x = 3 1 ',v = 22 -t³ t2 with 7 ≤ t ≤ 8.

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Q: Let P be the point with Cartesian coordinates (6,9), and C be the plane curve with parametric…

A: The parametric equation,x=t2-t and y=2t3-1123

Q: Show

A: Please refer to the image below

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A: Solution :Without odd-even…

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Q: An investment of $18,000 was growing at 6.5% compounded semi-annually. a. Calculate the accumulated…

A: In this question we have to find the following given Compound Interest.

Q: Find the transition points. y = 4x7 - 56x6 (Use symbolic notation and fractions where needed. Give…

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

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Q: Calculus Please Show

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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…

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A: Let's find area of the sector.

Q: Find a particular solution of =(x-1)² if y=-21 when x=-3. dy dx

A: Given differential equation is;…

Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

A: