The figure here shows triangle AOC inscribed in the region cut from the parabola y = x² by the line y = a². Find the limit of the ratio of the area of the triangle to the area of the parabolic region as a approaches zero. y = x? c/3=c° a² ( -a, α) (a, a²) -a

Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to…

A:

Q: 12: A tangent to the circle x² + y? = 5 at the point (1,2) and th circle x? + y² – 8x + 6y + 20 - A)…

A: Given that  A tangent to the circe x^2+y^2=5 at the point (1, 2)

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes A units apart.…

A: To show: That the surface area of the band is 2πRh. Given: The shaded band is cut from a surface pf…

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: A circle with radius 1 centered at (0, ) is tangent to two points of the parabola y = a². What is…

A: We have to find the area of the shaded region.

Q: The figure shows the graphs of the functions y1= x, y2= 1/2 x3/2, y3 = 1/4 x2 , and y4 = 1/8 x5/2 on…

A: Given: y1=x1y2=12x32y3=14x2y4=18x52On the interval 0,4

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y =x2 4 In(x),…

A: Given curve is y=14x2-12ln(x) Differentiate with respect to x. dydx=x2-12x

Q: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

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Q: The graph of x+y = 4 is an ordinary right cireular cylinder. Indicate axis of the eylinder lies…

A: The equation of right circular cylinder is given by  x2+y2=4

Q: 29 In the figure, the tangent to the circle at T cuts a chord AB produced at C. la) Prove that ATBC…

A: This is a problem related to the geometry side. Based on the general formula we will prove and solve…

Q: Let L be a tangent line to the hyperbola xy 32 at x3 Find the area of the triangle bounded by L and…

A: Find the equation of the hyperbola,

Q: Consider F and C below. F(x, y) = x2 i + y² j C is the arc of the parabola y = 2x2 from (-1, 2) to…

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Q: T. 9. TO = PO 10.Sector of a circle is the region bounded by two radii and their intercepted arc.

A: here we check whether the given statement is true or false.

Q: 2. KS is tangent to the circle at T. Secant KR contains P, the center of the circle. PR and PT are…

A: Firstly draw a circle with center P Now draw a tangent KS at point T

Q: Given the path C that is the line segment from (-4; 0) to the origin, and the curve y = 2x² from the…

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Q: The area of a cylinder sector with radius r and central angle of radian measure 0 is A = r20, and…

A: If the area of the sector is 1 sq. unit, then A=112r2θ=1θ=2r2          ...(1)

Q: Let L be a tangent line to the hyperbola xy=4 at x=9 Find the area of the triangle bounded by L and…

A: Compute the tangent line as follows.

Q: Question 6 of 10 Sketch the domain of f(x, y) = Vr +y? - 4. Use solid lines for portions of the…

A: We to sketch the graph of domain

Q: A point on a rolling circle of radius traces out a cycloid, which can be parameterized by c(t) = (Rt…

A: We have to show  that the length of this arch is always four times the diameter of the rolling…

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Q: Consider F and C below. F(x, у) 3 х2 і + у? ј C is the arc of the parabola y = 2x² from (1, 2) to…

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Q: 2. In the circle shown below, 3 points UV is a tangent, and UY is a secant. They intersect at point…

A: Consider th figure such that length of tangent UV=8, UY is a secant which intersect the circle at…

Q: B Fig 1 1 y = (3x)3 A I. Find the co-ordinates of A and B X II. Find the area enclosed by the curves…

A: Please see the below picture for detailed solution.

Q: 5. Find the total length of the curve r-4 (1-sin e) from 0-90° to 0-270° and also the total…

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Q: Vf(x, y) = 4y sin(xy)i + 4x sin(xy)j, F = V f(x,y), and C' is the segment of the parabola y = 5x²…

A: According to the fundamental theorem of line integral, for a smooth curve C given by r→t, a≤t≤b,…

Q: The plane x = 1 intersects the paraboloid z = x2 + y2 in a parabola. Find the slope of the tangent…

A: Given that the plane x = 1 intersects the parabolic z = x^2 + y^2 in a parabola.   So,…

Q: Find the area of the specified region. Shared SE by the circle r= 5 and the cardioid A) B) = 5(1+…

A: This problem is related to application of integration

Q: If C is a circle of radius 9 centered at the point ( -5, 5 ), then evaluate $ (2y – esin ( x ) ) dæ…

A:

Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = 2x² from (-1, 2) to…

A:

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

A:

Q: items 12-15, consider the region bounded by the curve y = cosx and the x-axis, where 0 ≤ x ≤ What is…

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Q: Given the figure: 23)The area of R2 using vertical strip is given by A. -xkx А. С. R1 В. (x-x kdx D.…

A: As per the guidelines,we are suppose to answer only one question ( out of 27 and 28 question)…

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes h units apart.…

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Q: II. Draw a sketch of the given arc C and evaluate Sc [(x² − 2y)dx + (2x + y²)dy]. → 1. C is part of…

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Q: The diagram shows part of the curve y? = x+1 which intersects the axes at A and B. The area of the…

A: given,

Q: 29. Let C be the quarter of the unit circle in the first quadrant, traversed coun- terclockwise from…

A: Explained below

Q: The area R in the plane is limited by the curves given by x = y^2 +2, y = x − 4 and y = 0, as shown…

A: Given Data: Equation 1: x=y2+2 Equation 2: y=x-4   The intersection point of curves of equation (1)…

Q: (b) Consider the cycloid C parametrized by x = t – sin t and y = 1 – cos t, for all real t. Find…

A: Solution x= t-sint, y =1-cost C(0) = (0,0) C(pi) = (pi-sin pi, 1-cos pi) = (pi, 2) C(2pi) = (2pi-0,…

Q: The shaded band shown to the right is cut from a sphere of radius R by parallel planes h units…

A: Given data:  The radius of the circle is "R". The equation of circle with radius "R" is given by…

Q: 2x y dA, D is the portion of the region between the circles of radius 2 and radius 5 centered at the…

A:

Q: A semicircle with diameter PQ sits on an isosceles triangle PQR to form a region shaped like a…

A: Let r be the radius of the semicircle, let x be the length of the two equal sides of the isosceles…

Q: The curve C is the circle of radius 19 contained in the plane z = 19 and centered around the z-axis,…

A: …

Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: Any help will be useful.

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = =x² - 1 1,2…

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Q: In the figure to the​ right, the equation of the solid curve is y equals StartFraction secant…

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Q: Question 4. Find the absolute maxima and minima of f (r,y) e- (+ y) on the closed triangular plane…

A: An absolute maxima is a point where the function obtains its greatest possible value. An absolute…