Eliminate Band a for the relation. x=Bcos(wt+a) in which w is a parameter. *

Q: How many independent variables does the function r(t) = ⟨ƒ(t), g(t), h(t)⟩ have?

A: Given that the functions f, g, and h, all depend on t. t is independent So there is only one…

Q: Which of the following is the domain set of the function f(x.y)=arcos(x² +y² –3)+In(x² +y² -3) ? ()…

A: The domain of logarithmic function log x is x: x>0 The domain of inverse trigonometric function…

Q: 2 T= {(x, y): y = x2+4

A: The given relation,   T=x,y: y=2x2+4

Q: Q2: Find the streamlines corresponding to: f(z) = 2 = z(z)-¹ z = x+yi, z = x - yi

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Q: Find fy fy and f, and evaluate each at the given point. f(x, y, z) = x²y³ + 2xyz – 7yz, (-2, 1, 2)

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Q: Which of the following is not a function of ƒ : R² → R? A. f(r, y) = e™y B. f(r,y) =1 C. f(r,y) =…

A: Here the function is defined from R2 to R. Therefore domain is R2 and codomain is R.

Q: (b) Use the chain rule to show that if g is differentiable and g(x) # 0 then -d (æ) 9(x)?² %3D

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Q: PV = k Y. Make P the subject of the relation T. %3D

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Q: Find f, and f, and evaluate each at the given point. y' f(x, y) = arctan (-) (4, -4) fx(X, y) =…

A: Given query is to find the partial derivative at given point.

Q: Find fy and fy, and evaluate each at the given point. f(x, y) = arctan(), (2, –2) fy(x, y) = f,(x,…

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Q: Find (a) ker(T) and (b) range(T).T: R3→R3, T(x, y, z) = (x + y, y + z, x − z)

A: Given: Transformation: T(x,y,z) = (x + y, y + z, x − z) The transformation in matrix form is written…

Q: Given the function f (x, y) = x + cy² – x, which of the following statements are true? I) The points…

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Q: 24. Given that the point (a, 462), a 20, is on the function y = f(x), which of the following is a…

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Q: Find fx and f and evaluate each at the given point. Fy f(x, y) = arctan 2), (6, -6) f,(x, y) = 5,(x,…

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Q: Suppose utility function takes the following form: uz = u(c¿, m,, l;) = (c;m¿)'l&.

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Q: draw a dependency diagram and write a ChainRule formula for each derivative. ∂w/∂s for w = g(x, y),…

A: Given:  w=gx,y, x=hr,s,t, y=kr,s,t To find: The dependency diagram and chain rule formula for…

Q: Write a chain rule formula for the following derivative. for u = f(p, q); p = g(x, y, z), q = h(x,…

A: Given a function u=f(p,q)

Q: B-- If a m.g.f of X is as follows: M, (t)= (1-21)-7 , find E(x) and V(x).

A: Explanation of the answer is as follows

Q: Given f(x, y) = 6,/3x* + 5y + 4xy°, find f-(2, y) = %3D fy(x, y) = %3D

A: Solution:

Q: Recall the relation between degrees Celsius and degrees Fahrenheit: F = 1.8(C + 32) X and Y are…

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Q: Find the interior, closure, and boundary of E = {q EQ : 0<q<}.

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Q: Find f, and f, and evaluate each at the given point. fx, у) - arctan(), (2, -2) fx(x, y) = ,(x, y) =…

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Q: 3: Assume that g(s) is an increasing function and define f(x, y) = g(x² + y²). Show that the angle…

A: Use definition of angle between vectors and gradient of function

Q: Which of the following is the domain set of the function f(x.y)=arccos(x² + y² -3)+In(x²+y² -3) ? ()…

A: Given:            f(x,y)=arccos(x2+y2−3)+ln(x2+y2−3)

Q: Determine the global extreme values of the function f(x, y) = 2a³ + 2x?y+ 5y², x,y > 0, x + y <1…

A: Consider the function: fx,y=2x3+2x2y+5y2…

Q: Given a function f(x, y, z) = ryz° +z°yln (z) – z'y? + 4, find: of (1,2, 1) = (1, 2, 1) = (1,2, 1) =…

A: Given problem based on partial derivative.

Q: given : y=xcos2x determine y'''(x) and y'''(π)

A:

Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: 2. Let f(x,y)=xe" and find a) fx, fyr fy

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Q: x2 If w = x".f then show that: + y², X. Wx + y. wy = nw.

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Q: Determine r (x) if r(x) = (arccot(x))".

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Q: Find fayr. f(x, y, z) = r*y"s* + xy' + y°z

A: The given function f(x,y,z)=x3y5z8+xy9+y3z

Q: dz Draw a dependency diagram and write a chain rule formula for and given the functions below. z=…

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Q: or function By – k1 z) + ay (kz y + z) onal, then the values

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Q: Find f, and fy, and evaluate each at the given point. f(x, y) ху (2, –2) X - y ,(X, v) = ,(x, v) =…

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Q: Which relation is incorrect: a. i.j = 0 d. j.k=i b. ixj=k e. ii 1 c. ixi=0

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Q: Find fy and fy, and evaluate each at the given point. f(x, y) = arctan(), (6, -6) fx(x, y) = f,(x,…

A: Given that: f(x, y)=arctanyx

Q: The range of the relation S from R to R given by S= {(x,y) ER? y 2-x) is. O a. (-x,0] O b. [0, x) O…

A: Domain of function: It is collection of all those points for which function is well defined. Range…

Q: 2. Let fx(X) va+I, Where x > b and a and b are positive parameters. Find E(X) and Var(X).

A: See the handwritten solution

Q: Find a function r(t) that describes the line segment from P(1,6,1) to Q(0,6,3) (inclusively). r(t) =…

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Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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Q: a. find g(x), h(y), f(x|y), and evaluate P( < X < |Y = }) %3D

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Q: The graph of fo- is concave down on interval (-1,1) A (0,1) B (-0,0)U(2,00) .C (-x,-1)U(1,00) .D

A: The intervals where f(x) is concave down, the tangents drawn on the curve lie above the curve.

Q: (c) Eliminate B and a from the relation, y = Bcos(wx + a). In which w is a parameter (not to be…

A: The differentiation of y=p sin(qx) with respect to x is defined as y'=pq cos(qx) .

Q: bo Find (xT x)" xT y where, b2 40 ら子 112 45 54 118 54 %3= 128 50 55 60 121 60 66 126 65 59 136 70 61…

A: Here, we have X=14057145541505415560160661655917061175581805918556   and…

Q: Find the lengths of the functions of y over the given interval. y² + 1)*¨ from y = 1 to y = 3 61/3…

A: Here we need to find the length of curve

Q: Differentiate implicitly the relation x³ + xy² = 2y³ – 4 to find y'. Then evaluate y'at (-1,–1)

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Q: Find f, and fy, and evaluate each at the given point. 'y' f(x, y) = arctan(), (2, -2) f(x, y) =…

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Q: The coefficient of correlation between X and Y is and ož = a, ož = 4a, and %3D %3D o = 114 where Z =…

A: Given that Z=3X-4YSo,…

Q: Eliminate the parameter t: x = (v0cosa)t, y = (v0sina)t-16t2

A: *to find:- equation in the form of x &amp; y only, by eliminating the parameter t.