Integration by Partial Fractions. Integration by Partial Fractions. We know that a rational function is a ratio of two polynomials P(x)/Q(x), where Q(x) ≠ 0. Now, if the degree of P(x) is lesser than the degree of Q(x), then it is a proper fraction, else it is an improper fraction. Because the partial fractions are each simpler. This can help solve the more complicated […]
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Category: mc
Integration (Basic)
Integration is summation of function. Integration is a way of adding functions to find the sum of functions, also we find equation of curve. As well as Applications are area under the curve and volume. It can be used to find areas, volumes, central points and many useful things. it help you practice by showing you […]
Derivative curve
This post about sketching of derivative curve from function curve. Given the graph of a function y = f(x) a standard approach is to identity intervals over which the graph is increasing, another intervals over which it is decreasing, and points at which the tangent line is horizontal. Derivative curve
Optimisation – 3
Process of finding optimal value of function at maximum or minimum value of the curve. It also give greatest or least point. Optimisation
Optmization-3
Process of optimisation means optimal value of function at turning point (maximum or minimum ) value of the curve. Therefore second derivative use to find greatest or least value . Also it show greatest value. Optimization
Derivative
First derivative for stationary point of the curve. If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. Second Derivative 1. If , then has a local minimum at . 2. If , then has a local maximum at . The extremum test gives slightly more […]
Discontinuity and Limit
An infinite discontinuity exists when one of the one-sided limits of the function is infinite. If the two one-sided limits have the same value, then the two-sided limit will also exist. Discontinunity and limit
Differentiation of function
The Differentiation means change in one quantity with respect to change in other. It also give of derivative of function . It also gives gradient of tangent of curve at a point. For differentiation use Power rule. Another differentiation is process for finding rate of change quantity. Rule of differentiation
Differentiation (Chain Rule)
Differentiation by chain rule for composite function. For differentiating the composite functions, we need the chain rule to differentiate them. If f is a function of another function. Chain rule also applicable for rate of change Chain Rule
Volume of Solids of revolution
Volume of solid of revolutions of a function, y=f (x), on an interval [a,b]. When we rotate this curve about a given axis we get the surface of the solid of revolution. Similarly Disk method. If the axis of revolution is the boundary of the plane region and perpendicular to the axis of revolution. Therefore Solid of revolution. A […]
