Find the maximum and minimum values of the function f(x) = x squared minus 4x plus 7 on the interval [0,3].
State the definition of continuity at a point. Is the function f(x) = |x| continuous for all real values of x?
If A and B are two 2×2 matrices such that A times B equals B times A, prove that the determinant of A times the determinant of B equals the determinant of B times the determinant of A.
Define an equivalence relation. Give an example of an equivalence relation on the set of real numbers.
Describe the mechanism of the addition of hydrogen halides to alkenes. What is Markovnikov’s rule, and how does it apply in this context?
Explain Raoult’s law for ideal solutions. How does it apply to a mixture of two volatile liquids?
What is the packing efficiency in a crystal lattice? Compare the packing efficiency of face-centered cubic and body-centered cubic structures.
Explain how soaps are different from detergents. Describe their cleansing action.
Define the term polymer. Differentiate between thermoplastic and thermosetting polymers with examples.
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