Calculus Problem Solving Techniques and Formulas
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Taylor Polynomials and Derivatives
Start by finding the derivatives of f(x) as needed. In the example question, it wants the degree 3, so we calculate up to the 3rd derivative, f'''(x), and then use the formula.
Solving Differential Equations
The equation ds/dt = sin(t) shows us that it is a pure time differential, meaning taking the integral of ds/dt will get us s(t). Since we know s(0) = 0, we use this to find the constant C. Once found, substitute it into s(3), and you have solved the problem.
Euler's Method for Numerical Solutions
To use Euler's Method, create your table with x moving at the rate given as Δ. Use the initial points and the formula provided. If given a function f(x), find the derivative. If already given a derivative or dy/dx,... Continue reading "Calculus Problem Solving Techniques and Formulas" »