Find the curvature K of the curve given below. r(t) = ti+8t²j+2tk

Q: Two elves can make 5 toys in 10 minutes. How many toys can 3 elves make in 20 minutes?

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Q: Find the volume when the following region is rotated about the y-axis: y = √4x², y = 0, x = 0.

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Q: Find the definite integral that will compute for the area of the region bounded by y = tan x, x = 0…

A: We can find the area bounded by the curve .

Q: 1 n (Inn)3/2 Σ(-1)". n=3

A: Given: Here, an=1n(ln n)3/2≤1n(n)3/2=1n5/2. So, the given series is absolutely convergent by the…

Q: Prove, using integration, that the volume of a sphere with diameter "d" is πYd³ 6

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Q: Solve the following linear systems of differential equations.

A: As per as our guidelines i am supposed to answer only three part of this question Please repost…

Q: The graph of y = f(x) is shown. Use the graph to answer the question. Is f continuous at x = -4?…

A: The graph of the function y = f(x). With the help of this graph, we have to show that, Is the…

Q: Find the volume of a sphere pyramid of height "h" and base edge of length "a"

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Q: Prove the identity. tan 0 1+ tan ²0 2 sin 20 To verify the identity, start with the left side and…

A: Basic question of trigonometry.

Q: Evaluate fx and fy at the given point. f(x, y) = e¹³y sin(x), (π, 0) fx(π, 0) = (No Response) fy(π,…

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Q: prove that :: 2) (1+i) (1-1)² = 64

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Q: Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also,…

A: Please see the below picture for detailed solution .

Q: 5. j(4x²-5x+4)*(8x-5)dx 6X dx x ²-5

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Q: Calculate the double integral. 7x S₂ x ² + x²0² +y dA, R= [1, 4] x [0, 1]

A: Explained below

Q: Question 2 i 1: a)' Solve the following linear system in detailed, by using Gauss-Jordan…

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Q: Rewrite the following equation with the variables separated. 3xy' + 2y = sin(y). dy (sin(y)+2y) O O…

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Q: For the IVP, y'=f(x,y), y=yo, x=xo, iff and df/dy are continuous discontinous defined undefined then…

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Q: Find the exact value of the expression in radians and degrees. -¹(2) -1 sin Find the exact value of…

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Q: x² - 2x x3 3x² - - dx -In 1x³ 3x² 1 + C Option 1 Option 3 - -In 1x³ 3x² 1 + C In 1x³ 3x²1+ C Option…

A: SOLUTION-

Q: The figure to the right shows four regions bounded by the graph of y=xsin x: R₁, R₂, R3, and R4,…

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Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: Evaluate the double integral. Sxy² da, D is enclosed by x = 0 and x =

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Q: 16. Determine whether the statement is true or false. If it is true, explain why. If it is false,…

A: The solution is given below

Q: For f(x, y)= e sin(25x), evaluate fy at the point (77, 0). Of,(7,0)=50 O fy(7,0)=0 Of(7,0)=51…

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Q: 2. Integrate the rational function below without using partial fraction decomposition. S -dv

A: Integrate the rational function below without using partial fraction decomposition v2/(v6-1)

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

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Q: multiple of a and c: =b/(n^3) c = b/(1 + n^2) S 1 du au²+bu+c

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: The given function,   cosx+tanxy+4=3

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = x4 -…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: The function shown in the graph below is increasing on the interval [1, 5]. The interval will be…

A: topic- Riemann sum using left and right endpoints

Q: Find the double integral that will compute for the area of the region bounded by x = y² and x = 4.

A: The given curves are; x=y2 and x=4 So, the bounded region is as shown below.   As we know that;…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: P(x)=92x-x^2-1760 find limx->40 P(

A: Apply the limits and find the value

Q: √(3x − 5)(x² + 1)da

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Q: Graph the function and the indicated tangent line. Graph f(x) = -4x2 and the tangent line to the…

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Q: Find the total differential. w = e²y cos(7x) + z³ dw = (No Response)

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Q: find a set of parametric equations of the line through (2,8,3) and (11,20,21)

A: The line through the points (2,8,3) and (11,20,21)

Q: 16. M8 Σ n=1 –3η + 1 2n + 3 4η

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Q: The area of an ellipse with axes of length 2a and 2b is given by A = Tab. Approximate the percent…

A: Concept: We have given the Area A=πab Here the length a is increasing by 2% which is daa=2% Here the…

Q: e −1 -1 lim (−1) t⇒0 t

A: Use limit expansion

Q: Find the derivative of y with respect to the independent variable. y = 2ln 2t 2 In 2 t OB. 2In 2t In…

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Q: Find the radius of convergence, R, of the following series. Σn!(7x - 1) n = 1 R Find the interval,…

A: Here we have to find the radius and interval of convergence.

Q: Find the indefinite integral using any method. (Use C for the constant of integration.) (sin(0) +…

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Q: The region is bounded by the curves of y = x² and x = y². Find the integral in line y = -1. Use…

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Q: Find the critical points of the given function. a) f(x)=√x²-4 b) f(x)= |3x +21-1

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Q: ind the definito integral that will computo for the area of the region bounded by y-2 ln x v-0 andy…

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Q: 4. If f is a coordinate system on a line /, determine whether or not each of the following functions…

A: We need to determine whether each will be a coordinate system or not.

Q: [4x 4x csc (4x) cot (4x) dx =

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