Find the aven bounded by y=x and y =x+2

Q: Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

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Q: Let f(x, y) = 4æ? - 4x – 7y + 2y² + 10xy List the critical point: Preview

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Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Find two nonnegative numbers x and y such that xy 56 and 7x + 2y is minimized. y =

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Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: Show that | S f(2) dx| < Sa \f (x)| dx.

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: Use chain rule to find az at (u, v) = (1, 1) if

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Q: Let f(x, y) = y³ + x² – 3y Prove that the Critical points are (0,1), (0, – 1),

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Q: Let f(x, y) = (- (3z + y))°. Then

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Q: Use the chain rule to eX Pressdy intermsof X and Y: and t= at X=2

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Q: Find the artho gon al traje eteries to c°y" - 4y + x*

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Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: Find the orthogonal trajection of the family of y=ax

A: In mathematics an orthogonal trajectory is a curve, which intersects any curve of a given pencil of…

Q: Let f(x, y, z) = x²y°z – xyz², and compute: (a)

A: In this question we will use basic of vector  calculus i.e gradient of any function and curl of…

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: let f( x, y) = x cos xy then fx is: is: O - sin y O -y sin xy cos (xy) - xy sin (xy)

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Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: Let f(x, y, z) = -2xy − xz + 3yz + 1⁄x² + 3y² + z². - The set of critical points of f is

A: Given: fx,y,z=-2xy-xz+3yz+x22+52y2+z2 To find: The set of all critical points of f.

Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

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Q: Find Positive nombers X$ Y Such that X+y = 78 and 24xy a is maximized

A: To find two positive numbers 'x' and 'y' such that,  x + y = 78     =&gt; y = 78 - x And such that…

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: Let f(r, y) = 5x-+ 2y + 4y- 8ay List the critical point:

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Q: 6. If F(x) is defined by cx²+2x F(x) = esin(t) dt Determine F'(x).

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Q: Find two nonnegative numbers x and y such that xy = 60 and 5x + 3y minimized. x =

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Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

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Q: What is the antiderative of xysin((x^2)y)?

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Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

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Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: Let f(x, y, z) = xyt + z3 and x = st², y = s³t² , and

A: The given function is fx,y,z=xy4+z3 and the values of x, y, and z are st2, s3t2, and s2t2…

Q: Let f(r,y) r+ 12ry+12y. Find all the critical values and claesify them.

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Q: Find Critical point of f(u)=ue^(u^n )+ln√(u^n+n), Where n=822

A: f(u)=ue^(u^n )+ln√(u^n+n), Where n=822

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Determine whether the work done along the path C is positive, negative, or zero. negative positive…

A: Consider the provided graph, Determine whether the work is done along the path c is positive…

Q: Let f (x, y) = y³ + x² – 3y | Prove that the Critical points are (0,1), (0, – 1), (1,1), (–1,1),…

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Q: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

Q: Find the Wronskian for the set of functions.{x, x2, ex, e−x}

A: Given information: x, x2, ex, e-x The Wronskian is given by the following determinant.…

Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

A: Here, ∂ represents the partial derivative, which means when differentiating with respect to x,…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.