Find the midpoint M of CD M = (, ) X1+X2 Y1 %3D 21 C = (-2,-10) D = (-6,0) M = ([ ? ], [ ]) Enter the number that belongs in the green box. Enter

Q: Integrate F(r)= [e2*, e²y,e²²] along the helix that cuts the z-axis at c.

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Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 4 10 In(x) dx, n = 6

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: Find the maximum height above the xy-plane of a point on r(t) = (e1 , sint, t(4 - t))

A: Maximum height above the x-y plane will be the maximum value of z .So we will take z parameter of…

Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: 4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y >…

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Q: Q2: A-The Trapezoidal rule for roodx 5 and Midpoint rule /)dx=4 What value does . Simpsons rule give…

A: 1st we will find relation between trapizoidal , mid point and simpson rule . Then will use this…

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = Y 04 1+²dy rotating

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: y = VT, y = 2 - x and r O about the x-axis?

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Q: On what interval is the curve y = 0, v- [ t2 dt t2 +t + 2 concave downward?

A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Find the length of the curve y = S Vcos t dt, 0 <x<n.

A: Given; The curve y=∫0xcost dt,      0≤x≤π .

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: Hn obfect Is moving along the X- axis with acceloration givon by at) =Q +42zt. TF V l0) =1 and…

A: Given query is to find the displacement function for the acceleration given.

Q: y = x* + 1, y = 0, x = 1 around the ar axis.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: f(x) = 3x²+x+7. Approximate fo trapezoids. O a. 60 Ob. 44 Oc. 30 Od. 22 f(x)dx using the trapezoidal…

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Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Given the DE. 3dy + ydx = (1-2x)y4, Rewrite the DE into Linear Form at v O dx-v = 2x+1 dx-v=2x-1…

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Q: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: Find the image of the line z =3 +iy under f(z) = e

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32…

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Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.