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What are the important points to graph #f(x)=2 sin (x/3)#?

Answer 1

Important points to the graph are #x# = (#0#, #(3pi)/2#, #3pi#, #(9pi)/2#, #6pi#, #(15pi)/2#, ....). Note that these are all at #(3pi)/2# intervals and maximum and minimum value is #+-2#.

When we draw sine graphs, we do not try to plot all the points but initially only important points.

In the graph #f(x)=sinx#, maximum and minimum value is taken as #1# (at #x# = #pi/2#, #(5pi)/2#, #(9pi)/2# ...) etc, and #-1# (at #x# = #(3pi)/2#, #(7pi)/2#, #(11pi)/2# ...).

Apart from that #0# value is taken at (#0#, #+-pi#, #=-2pi# and so on).

These form the important points.

In #f(x)=2sin(x/3)#, maximum value taken is #2# at #x# = #(3pi)/2#, #(15pi)/2#, #(27pi)/2# ...) etc. and minimum value taken is #-2# at #x# = #(9pi)/2#, #(45pi)/2#, #(81pi)/2# ...) etc. and #0# value is taken at (#0#, #+-3pi#, #+-6pi# and so on).

Note that these are all at #(3pi)/2# intervals and maximum and minimum value is #+-2#.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.