1) Let F = (xyz, sin(y), e") a) Find V x F. Check your answer. b) Find Vo F. c) Is conserv:ative? F conservative? Explain briefly.

Q: BA)Find normal line and parallel plane to the function f(x, y, z)=x√yz + 6 At point (-3,1,4).

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Q: f(x) = 5 sinx + 4 cos x, on (-T, π) a) Determine the intervals on which f is concave up and concave…

A: The given function is fx=5sinx+4cosx, on -π,π. To Find: a) Determine the intervals on which f is…

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: Let F (r, y, z) = sin y i+r cos yj- sin z k.

A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

Q: a) Show that the work performed by a constant force (not necessarily in the direction of motion) can…

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Q: 5) Let f be differentiable at a. Show that f(z) is differentiable at a if and only if f' (a) = 0.

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Q: is The functionFIO-Vx4iscontinusus onR. It cosă

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Q: 8.) Let fx)= 2x³+3x +4 Use the limif definition of the derivative to calculate the derivative of f:…

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Q: find Jw E fur the f ollowing au d fuuctivus : X +y tan" Xャう csC ( + y x* + y z`) W : CSC

A: Given : some functions To find : partial derivatives of given functions

Q: 10. r(t) = F(t) x G(t), where F(t) = t³i – tj + tk, G(t) G(t) = 3√/ti+ 1 t + īj + (t + 2) k -j 1

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Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: (d) Find the value of that makes the following two vectors parallel to each other: a=-zi+3j 6=3i-j…

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Q: Jige If f(2) =-3, g(2) =4, f' (2) =2, and g' (2) =, d. then dx -21 16 9. 16 -13 16 29 16 6 jp 3…

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Q: 23. b) c) d) e) f) Calculus word bank. Fill in the blanks using the correct answer using words. The…

A: Here's how you can fill in the blanks using the words from the word bank:d) If f′(x) changes from…

Q: Evaluate

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Q: »[32° dx = 3x² A) 6 B) 7 C)8 D) 9 타 10 xdx A) - B) - Suppose F and G are continuous functions with…

A: We have to answer the following...

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: Show that the Cobb-Douglas function F(x, y) = bx" y" satisfies the equation ƏF ƏF + y (n + m)F(x, y)…

A: Given that the Cobb-Douglas function F(x,y)=bxnym We have to satisfies the equation…

Q: Which of the following functions maps the red function (y=x)onto the image function? a) y = -x+2|…

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Q: Use Green's Theorem to evaluate F = (xy + y²)i+ (x – y)j | (1, 1) x = y² y = x² (0, 0)

A: we have to evaluate the following by using greens theorem

Q: вс est. et sinut dt wt

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Q: TT 4 3. f(1 + sinx) dx + f(1 + sinx) dx 0 TU 4

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Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: re sin + y2

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Q: Show that u is s is mmomphie to F' Lt T:VaV (V is as abore let Tuct) zt u'Le) 2 the derivative im…

A: Let F=ℝ and V=a+bx2+cx4 :a,b,c∈ℝ . Show that V is isomorphic to F 3. Let T: V→V defined as follows,…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.