18. Let P denote the path parametrized by F(t) = (1/2), 0 ≤ Compute ſp F·dF, where F (x, y, z) = ( x-y 3+y² 62 0 ≤ t ≤ 2.

Q: 16) Which function will shift y= vx right 4 units and up 1 unit? A) y = Vx + 4 +1 B) y = Vx + 1 C) y…

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Q: f (x) = x³ – 3x %3D 34 - the distance between the local extreme points of the function OA) V5 B) 2…

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Q: 1. Given a function w = f(x,y, z) = -x² – y² + z. a) Find the domain and range of the function. b)…

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Q: 13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for:…

A: Note:-Since you asked multiple questions which are not interlinked to each other, according to our…

Q: kh= •a+h [ath 2xƒ(1) √ √ 1 + (ƒ' (1))² dt 2лf(t).

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Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

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Q: Consider the function f(x, y) = 2x²-3xy + 8y² + 2x - 4y +4 at the point P(-2,1). a) Find a vector…

A: Let  be a function, thena) the gradient  gives the direction of the steepest ascent at point…

Q: A particle moves along the x-axis with acceleration give by a(t) = 2t - 10 +12/t for t >= 1.  A)…

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Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: F being a function of two variables;  F( x= az, y=bz) z = z(x, y) defined by the relation a∂z/∂x…

A: It is given that F is a function of two variables x and y and is given by Fx=az, y=bz. Here, z=zx,y.…

Q: f(x, y) = xy(3-a-y) OA. (1, В. О в. (0, 1) O C. (0,0) O P. (-3,3)

A: Given function is f(x,y)=xy(3-x-y) At first we differentiate it partially w.r.t. x and y and setting…

Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

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Q: Evaluate F.dr where F(x, v) yi+ejand C is the line segment from (2, 0) to (4,0). a) 0 b) 2 c) - 2 d)…

A: Try to identify line segment then apply on integral part

Q: Evaluate / = F dr where F [y+z, z+x, x+y] and C: r(t)= [t, sint, cost], from A:(0, 0, 1) to B:(T, 0,…

A: Answer

Q: c) Given a function $(x, y, 2) = 3x² + In (3y² + 1) + e* cos z. i. Find the directional derivative…

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Q: of lf" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only…

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Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: Let f(x, y) = 6x – 2ry and the point M(5, 9). Among all unit directions, there is a unit direction…

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Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

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Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

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Q: Find the displacement of an object on the interval 2 ≤ t ≤ 5 if its velocity is shown. V(Đ m 3 1 5 7…

A: Given: A graph of velocity-time.

Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Q.2) Determine the relative extrema of 1 f(x,y) = xy-y² + 2x2² - 2x

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Q: Find whether the function F= 5yz? i+(3x– 2)}+(x² – xyJk is solenoidal.

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Q: Compute F. dr where F (x,y) (6x + y) i+ (4y + x)j and C is a piecewise curve from the point (1,1) to…

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Q: 13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for:…

A: Note:-Since you asked multiple questions which are not interlinked to each other, according to our…