Validity of the limit
Prove the validity of the limit lim x->x_0 (ax+b)=ax_0+b by converting to a statement about sequences.
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Make up an example of a problem which features the terms below, and solve them. It can be a extremely simple straightforward problem.
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Suggest: f : R----> R is continuous, a, b are functions from R to R and are differentiable on R. g(x) = integral of f(t)dt with upper limit = b(x) and lower limit = a(x) the problem is to determine a general formula for the derivative of g at x
Use the method of variation of parameters to determine a general solution to differential equation: ty''+(1-2t)y'+(t-1)y=te^t given that y1=e^t and y2=e^t (ln t) are two linearly independent solutions to the corresponding homogenous equation.
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Determine the general solution of given differential equation. Provide largest interval over which the general solution is defined. Find out transient term.
Use reduction of order or formula to find a second solution
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