De modo informal, ¿Qué señala el Teorema Fundamental del Cálculo? a. Que la sumatoria infinita de los rectángulos viene a ser la integral definida b. Que el área bajo la curva viene a ser la integración definida c. Que la derivación e integración (definida) son operaciones inversas d. Que los problemas deben analizarse por diferenciales

Find the derivative of \( f(w)=\frac{3}{\left(w^{2}-6\right)^{5}} \)

Residues at Poles = Proof the Theorem Assume \( f(z) \) has the following form \[ f(z)=\frac{\phi(z)}{\left(z-z_{0}\right)^{m}} \] where \( \varphi(\mathrm{z}) \) is analytic and nonzero at \( \mathrm{z}_{0} \), then it has Taylor series representation

Residues at Poles - Example 1 The function \( \quad f(z)=\frac{z+1}{z^{2}+9} \) has an isolated singular point at \( \mathrm{z}=3 \mathrm{i} \) and can be written

June 2018 ZIMSEC Paper 1 Solve the equations: \( e^{2 x}=4 e^{2-x} \) giving the answer in exact form. November 2010 ZIMSEC Paper 1

Calculate the area under the curve defined by the function \( f(x) = x^3 + 2x - 1 \) from \( x = 1 \) to \( x = 3 \).