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Determine y′′ for x 2 + y 4 = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w
Evaluate the given limits, showing all working: Using first principles (i.e. the method used in Example 1, Washington 2009, Using definition to find derivative ) find the
Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket
Define a complete lattice and give one example. Ans: A lattice (L, ≤) is said to be a complete lattice if, and only if every non-empty subset S of L has a greatest lower bound
Arc Length - Applications of integrals In this part we are going to look at determining the arc length of a function. As it's sufficiently easy to derive the formulas that we'
A right triangular prism has volume equal to 288 cm^3. The height of the prism is 3 cm. One of the bases of the triangular face (not the hypotenuse) is equal to 12 cm, determine th
What is Faltings Theorem? Explain Faltings Theorem
Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ± tS x¯ x¯ = Sample mean S x¯ = s/√n S = standard deviation
Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov
Now that we've found some of the fundamentals out of the way for systems of differential equations it's time to start thinking about how to solve a system of differential equations
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