calculus curve sketching

Curve Sketching - The graph of a given function gives a visual presentation of the behaviour of the function involving a study of symmetry, rise and fall, region of existence, passage through specific points etc. The following points are helpful to trace the curve..

The graph of a given function gives a visual presentation of the behaviour of the function involving a study of symmetry, rise and fall, region of existence, passage through specific points etc. The following points are helpful to trace the curve..

The pattern of the curves repeats at an interval p . Therefore it is sufficient to sketch the curve form 0 to p..

Any curve or straight line whose distance to a given curve tends to a given curve tends to zero is known as asymptote. An asymptote may or may not meet the curve. It acts as the boundary for the graph of a function and helps in graphing the functio..

a) Symmetry about x - axis If the equation of the curve remains unaltered when y is replaced by -y, then the curve is symmetrical about x-axis. b) Symmetry about y-axis If the equation of the curve remains unaltered when x is replaced by -x then the curve is..

In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of dy/dx to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves...

In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The derivatives al..

The concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the values generated in the laboratory or collected in the field. We connect the plotted points ..

with this information, we sketch the graph as show ...

Functions Limits and Continuity - The concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the values generated in the laboratory or collected in the field. We..