Let a = (a, az); b = (b, ,b2) € R?, define the function %3D %3D d: R? x R? ---> R by d=(a, b) = |b,-a, I + do(az, b2), where do denotes the discrete metric on R. Prove that d is a metric on R?

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…

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Q: Which of the space curves describes the vector-valued function r(t) = (t + 15, e0.08t cos(t), e0.08t…

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Q: Which of the space curves below describes the vector-valued function r(t) = (t + 15, e0.08t cos t,…

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Q: 3. Find the divergence of U3 -e3 U1U2 U1 U2 -ēj + e2 + F 2uzu3 U3 if hi = U1U2, h3 = Uz. = U1, h2

A: Given the field , F=u12u2u3e1+u2u3e2+u3u1u2e3 and h1=u1, h2=u1u2, h3=u3 Divergence of F is given by,…

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Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 5tj + 2tk O Z -2 XX k k Z 5 5 5 2 2…

A: Given Data: rt=-ti+5tj+2tk   0,1 To Find the length of the given interval.

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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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A: Disclaimer: Since, you have requested for the answer of part 3, only part 3 has been answered.…

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Q: 8. let C be the curue space ret) = (e*,2et ,2et ),0s ts lnca) the rength of C is

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Q: Let be a curve defined by the vector function (t)= 6ti + çin 2t -cos 2+ k 3- and Find the moving…

A: Let C1 be a curve defined by the vector function R→(t)=6ti→+sin2tj→-cos2tk→. Find the moving…

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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.

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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,

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Q: 76 Find T, N, and x for the space curve r(t)=7i+j₁t> 0.

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Q: d (x, y) = (x - y)^2 does the function define a metric o

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Q: Find T, N, and k for the space curve r(t) = (7e'cos t)i + (7e'sin t)j + 4k.

A: Given data:  r(t)=(7et cost) i +(7et sin t) j+4k

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