ydx = x + Vy² – x² dy

Q: f(x)=10/17sqrt(6x^2+2x+6)= 10(6x^2+2x+6)^1/17, then df/dx =

A: f(x)=106x2+2x+6117

Q: sin² 3y 5. ye 3^cot3t

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Q: 3. The function f(x, y)= 8x' - /4x° +3y° is homogenous in x and y of degree 4. The function f(x, y) ...

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Q: Compute the indicated derivative. U(t) = 5.9t2 + 5.9; U'(4)

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Q: -sin20 + C , then f (0) =-cos20. 2 A True B) False

A: Solution: f(θ)=12cos2θ

Q: The augmented matrix of a linear system has been reduced by row operations to the form shown. Contin...

A: topic - solution of linear equations using matrices

Q: One the first day of class, a professor asks each student what country they are from orginally. What...

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Q: Find the volume of the solid generated by revolving the region enclosed by y = x2+1 and y= x+3 about...

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Q: 1- メー」 メ メ+ 2- you 3- 3+13 y= メー/3

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Q: Let f(x) = 8- 4x + 3x. Calculate the following values: f(a) =| f(a + h) =| f(a + h) - f(a) %3D %3D f...

A: Topic = Functions

Q: Use differentials to approximate the change in cost corresponding to an increase in sales (or produc...

A: Solution ) c = 0.075x2 + 6x + 2  with dx = 1  differentiate with respect to x  dc/dx = 0.075 × 2 x +...

Q: Consider the following differential equation. y"-y'-30y 0 Verify that the functions .-5x and 6x form...

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Q: Evaluate the definite integrals using properties of the definite integral and the fact that 4. 4 Lfe...

A: given : ∫-52f(x)dx=-3 , ∫24f(x)dx=8 , ∫24g(x)dx=8(a) ∫-5210f(x)dx=10∫-52f(x)dx=10×(-3)=-30 ∫-5210f(x...

Q: Sss*dx= [s 521²dx 5'52 dx A True B False

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Q: 7 13 Consider the series 4n n=0 a. The general formula for the nth partial sum is Sn Your answer sho...

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Q: Question 10 What are the coordinates of the endpoints of the focal width of the parabola (x + 6)² = ...

A: Topic = Coordinates geometry Correct option = C

Q: Q4. (a) Evaluate the definite integrals: (i) ſ(2 – 5/1 – x² }tx_ (ii) [sin 2x cos 2x dx (iv) [": 'V1...

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Q: 1. (2xy-tany)dx + (x² – xsec?y)dy = 0; y(1) = r 2. [4x°cos(xy)-x*ysin(xy)- ye" +3x²]dx -[x°sin(xy)+x...

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Q: x3(75 − 14x4)5 dx

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Q: Compute the resulting error in the function f (x) = x³ for value x = 2.38 with an error Ax = 0.005.

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Q: cot e*dx e2x +1

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Q: x*dy + (2.xy – y² }tx = 0 Let the substitution y=2; y=vx; dy=vdx+ xdv

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Q: Calculating Mass from Radial Density. Mass-Density Formula of a Two-Dimensional Circular Object. Giv...

A: Given: m=∫0r2πxρxdx  ...(1) And ρx=6x ; x=6   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 A...

Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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Q: se vectors to determine whether the triangle with vertices A = (1,–3,–2), = (6,–2, -5) is right-angl...

A: we know that if the dot product of two vectors is zero then the two vectors are perpendicular. there...

Q: The Center of Mass of a Thin Plate (region) Consider the region in the zy-plane bounded by the curve...

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Q: Find thlength of the curve.  Y=1/6(x^2+4)^3/2, 0<x

A: We have to apply arc length formula to solve the problem

Q: )ca) if vector as 6=2ナリーk Calculate axb and bxa. (b) Find The area of the paralletogrmais bounded by...

A: Area of parallelogram of the vectors a and b is a×b.

Q: yesin 3y* dy dy 5. csc 6y

A: The question is a little incorrect. I have modified the question a bit: the denominator should be: c...

Q: Determine the force due to hydrostatic pressure on a gate of an 8 ft tank filled with water (62.4 lb...

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Q: 2. Form the differential equation by eliminating constants a and b from y? = a(b – x)(b+ x) + 59.

A: y2=a(b-x)(b+x)+59

Q: Q/ Find the domain and range of the following functions メー」 y= 2y= メ+ 3+13 メー/3 3- 1,

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Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: topic - application of derivatives

Q: A projectile is fired straight up from a platform 10ft above the ground, with an initial velocity of...

A: Topic:- application of integration

Q: 2. lim f(x) and lim f(x) if f(x) = V4-x2 %3D X-2+ X→2- х-2

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Q: Center of Mass: Point masses in the plane. Suppose three point masses are placed in the ry-plane as ...

A: We find out centre of mass for the given system. Follow 2nd step.

Q: f (t) = 3 (t + 1) H (t – 1) |

A: Solution ) f ( t ) = 3 ( t  + 1 ) H ( t - 1 ) Formula  [ L g(t) H ( t - a ) = e-asL{ g( t + a ) } a ...

Q: 1. Let A, B and C be the vertices of a right triangle in R with hypotenuse BC. Let D be the point on...

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Q: Determine the standard equation of the parabola opening upward, with focus at (0,6) and whose length...

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Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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Q: Find the DE of each of the following by eliminating the arbitrary constants. y =Ce* +C2cos.x +C3sin ...

A: Herw we have to find the differential equation.

Q: What is the differential equation of the family of ellipses with their centers origin and their majo...

A: Let us solve the problem using the basic equation of ellipse  later we will use different methods to...

Q: Sketch the region bounded by the graphs of the equations and find the area of the region. y = cos x,...

A: The region is bounded by y=cos x and y=2-cos x, 0≤x≤2π

Q: Which of the following is not in the domain of cot(x)? Select all correct answers. Select all that a...

A: Note that:- Domain of cot(x) is R-{nπ , n∈Z}  Where is R is set of all real numbers and Z is set of ...

Q: S The graphs of the polar curves r1(0) = cos 0 and r2(0) = 2 sin 0 are shown in the figure above. (a...

A: The given curve are: r1θ=cosθ       and       r2θ=2 sinθ

Q: 8 -5 -8 Factor out (1 + z )° from (256z°+ 150z + 150z - 25z- 25z° + 3 + 3z1

A: Given:    256z-5+150z-4+150z-6-25z-2-25z-8+3+3z-10

Q: Consider the series > 5e". n=0 a. The general formula for the sum of the first n terms is Sn (5e( 1-...

A: This is a problem related to series calculation. Based on the simplified terms it was observed that ...

Q: Find the equation of the line tangent to the graph of f(x)= (In x)2 at x= 3. y%3D (Type your answer ...

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Q: II. Solve for the derivatives implicitly. 42 y-2x = 2 +4y³. + 4y³. =1 5. 6.

A: We can differentiate the derivative implicitly as below

Q: 2. x'dy+(2xy- y)dx =0 Let the substitution v=2; y= vx; dy vdx + xdv

A: