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Differential Geometry | Topology
2.A stone moves along the path x=t^3+1,y=t^3, z=2t+5, where t denote time. What is the component of (dp)/dt ?
3i+2j-2k
3i-2j+2k
3i+2j+2k
-3i+2j+2k
3i+2j-2k
3i-2j+2k
3i+2j+2k
-3i+2j+2k
Differential Geometry | Topology
Show that the set of rational numbers with the subspace topology of R is disconnected
Differential Geometry | Topology
Prove or disprove
1) every topological space is metrizable
2) any metric defined on X(is not equal to 0) induces a topology on X
1) every topological space is metrizable
2) any metric defined on X(is not equal to 0) induces a topology on X
Differential Geometry | Topology
Prove that the Hillbert space is separable
Differential Geometry | Topology
Prove that the boundary of a subset A of a metric space X is always a closed set
Differential Geometry | Topology
Give an example of a regular space that is not normal
Differential Geometry | Topology
Prove that the boundary of a subset A of a metric space X is always a closed set
Differential Geometry | Topology
a) Find the gradient of the curve at (2,-3)
b) what does your answer to part (a) tell you about the point (2,-3)
b) what does your answer to part (a) tell you about the point (2,-3)
Differential Geometry | Topology
1. Find the smooth curve (C1) realizing the shortest distance between two given points in a plan (usual Euclidean R2).
Differential Geometry | Topology
Let p= sin t i + cost j + tk, What is |dp/dt|?
a.\\(\\sqrt(7)\\)
b.\\(\\sqrt(2)\\)
c.\\(\\sqrt(3)\\)
d.\\(\\sqrt(5)\\)
a.\\(\\sqrt(7)\\)
b.\\(\\sqrt(2)\\)
c.\\(\\sqrt(3)\\)
d.\\(\\sqrt(5)\\)
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