Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y=3x2 , y=0, and x=4.3

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

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Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: x² 1) Let f(x) (Figure 24). Verify the X 1 following: (a) f(0) is a local max and f(2) a local min.…

A: Since you have posted a question having multiple subpart part as per guidelines we can solve only…

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: The population of a city is modeled by the equation P(t) = 357,512e0.25(t) where t is measured in…

A: We have to find how many years will it take for the population to reach one million.

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

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Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

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

A: topic- algebra

Q: 23. Test the series below for convergence using the Ratio Test. Σ n2²n 8n-1 n=1 The limit of the…

A: Here we have, ∑n=1∞n22n8n-1

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: Evaluate the double integral: 3 +9 Lo L₂ Y COS(2 (Hint: Change the order of integration to dy dx.) y…

A: The objective is to evaluate the double integral.

Q: (a) Find the exact area under the curve y = 1/x³ from x = 1 to x = t for t = 10, 100, and 1000. t =…

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Q: closed box with a square base is to contain 252 cubic feet. The bottom costs $5 per square ot, the…

A: Please refer to the image below

Q: Evaluate L L ³ xy² 1 3xy² dy dx.

A: SOLUTION-

Q: Determine if the function f (x, y) = if (x, y) = (0,0) is continuous at (x, y) = (0,0). If not,…

A: Use limit to find wheather function is continuous or discontinuous.

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

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Q: Let r(t) = t - sin(t) and y(t) = 1- cos(t) All answers should be decimals rounded to 2 decimal…

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. (a)…

A: Both integral is solved.

Q: Evaluate J (2a² y +9y³)dA, D is the region bounded by y www 33522 a. 5 O b. 4811 5 OC. None of the…

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Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

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Q: ds Find the complete solution of = 8t³ √s. dt

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Q: 7. ydx-xdy + xydy = 0 Ans: In²+ y = c

A: We have to solve differential equations

Q: II. Consider the circle C1 : r = 1 and the roses C2 : r = cos 2θ and C3 : r = 2 cos 2θ, each of…

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Q: smaller x-value larger x-value (x, y) = (x, y) = X X

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Q: Find the area bounded by y = x3 +6, y = x and y-6 www. -X.

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

A: Given differential equation is;…

Q: Consider the vector-valued function R(t) 1. Find the domain of R. 2. Show that R is continuous at t…

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Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂:r = 2-2 sin (in red) and let R be the…

A: Given that polar curves  C1 : r = 3  and C2 : r=2-2sinθ  we have to find all points of intersection…

Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

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Q: 3 [*² [b³ – y³]² dy

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Q: = Find the area bounded by the curves -x + y² = 8, x = -2y and y

A: Follow the procedure given below.

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

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

A: Solution of given question is written in below steps.

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

A: Explained below

Q: Find the area of the parallelogram with vertices P₁, P2, P3, P4 P₁ = (1,3,3), P₂ = (1,2,2), P3 =…

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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: Find the average value of the f(x) from z = 10 to z = 16 f(x)= √² - 100 I

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Q: Convert the Cartesian coordinate (-1,-3) to polar coordinates, 0≤ 0 0 r = 0 =

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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: If an investment grew to $13,500 in 3 years and the interest amount earned was $1,531.34, calculate…

A: To find out the compound interest.

Q: 7 x = R¹, ƒ(x):=· + 3√x² 1-x 1+x² +ea² +1 +π².

A: see below the answer and calculation

Q: True or false 1. √2 If cosh x = V, then sinh x = 2. It is possible for a function to have an…

A: Here we have to determine whether the statement is true or false.

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

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Q: 2x³ - 4x² − x − 3 dx x² - 2x - 3 zln |x+1| +31n|x - 3| + C Option 1 2 In x + 1-3 ln|x - 3| + C…

A: Given, ∫2x3-4x2-x-3x2-2x-3dx

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x- cos x (a) lim x/4…

A: According to the company rule we can answer only first question and rest can be reposted.

Q: 39 9. A curve with polar equation r = 6sin0+13cose represents a line. This line has a Cartesian…

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Q: Consider the position function s(t) = -4.9t +31t+24. Complete the following table with the…

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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.