Ik (X,d) Is a mete spate and kyo then show that di ex.y ) Kd (X)y) 1+kd (メッ) is a bounded metric on X.

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: cost-sint) √2 r(t) = (3e' cost)i + (3e¹ sint)j + 2k For the space curve below, T= i+ sint+ cost s!).…

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Q: the function is a metric of R: d(x,y) = sqrt(x^2−y^2);  x,y ∈ R

A: let z1=(x1,y1) and z2=(x2,y2) now, d(X x Y, d) is a metric space if 1)d(z1,z2)=0 if z1=z2 now, if…

Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

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Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

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Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: P(E) = 0.55, P(F) = 0.35, P(E U F)= 0.8 Find: a)P(E ∩  F)                      b) P(E^c) c) P(E^c…

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Q: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: 4 Suppose that f(x, y) = x4 + y xy

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Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: Find the limit 2yz lim (x,y,z) (0,0,0) x4 + y² + z² along the curve x = 2t, y = 3t², and z = 4t².

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose that f: R² → R² is a function such that f (1, 2) = the linear approximation. (Use syntax…

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Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: If f (s Continuous then on -fex) True or felse?

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Q: Let /: X →Y be a function, A, BC X and C, DCY. Show that: 1. f(AUB) = f(A) uf(B) 2. If AC B, then…

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Q: Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0, 0). b) Exists a point (xo,…

A: We are given the function fx, y=ln1+x2+y4. Our aim is to choose the correct option for the given…

Q: u = (x2y2)/(x+y), show that x(∂u/∂x) + y(∂u/∂y) = 3u

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Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x,…

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Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Consider f(x, y)=x2+4y2. Draw a contour map to show the level curves according to f(x, y)=k, where…

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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: 2. Find the limit of the following vector functions: а) lim (2eti + 6e-tj – 4e-2tk) t→ln 2 b) lim i…

A: Logarithmic and exponential properties,Differentiation formulas,l'hospital's rule,

Q: 6. Prove the divergence "product rule" identity: div(f G) = (Vf). G + f div(G) Hint: let the…

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Q: d (n, m): = 0 si n = m si n‡m 5-c(n-m)

A: Question seems wrong

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.