Example:
is a proper rational function. This can be expressed as are the partial fractions. \ The given proper rational function is resolved into two simpler rational fractions. Note that the denominators of the rational functions are resolved into facto..
is a proper rational function. This can be expressed as are the partial fractions. \ The given proper rational function is resolved into two simpler rational fractions. Note that the denominators of the rational functions are resolved into facto..Example:
Evaluate the integral..
Evaluate the integral..Example:
Evaluate the following integral The given integral is of the form (10). Using this formula, express Equating the coefficients of x and the constant term 2A = 5 4A + B = 3 2(2A) + B =3 10 + B = 3 Therefore Put x 2 + 4x + 10 = t so that (2x + 4)dx=dt ..
Evaluate the following integral The given integral is of the form (10). Using this formula, express Equating the coefficients of x and the constant term 2A = 5 4A + B = 3 2(2A) + B =3 10 + B = 3 Therefore Put x 2 + 4x + 10 = t so that (2x + 4)dx=dt ..Example 2:
The decay rate of radium at any point t is proportional to its mass at that time. The mass is M 0 at time t = 0. Form the differential equation and find the time when the mass will be halve..
Example 4:
Find the equation of the curve that passes through the point (3,- 4) such that the slope of the tangent at the point (x, y) on it equals ..
Find the equation of the curve that passes through the point (3,- 4) such that the slope of the tangent at the point (x, y) on it equals ..Example 2:
Form a differential equation by eliminatory the parameter A and B from the family of curves given by y = Ae 2 x +Be - 2 x..
Example 2:
Differentiate cos - 1 (2x+3) from first principle..
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