Discuss the continuity of `f(x)=sinxcosx`

Explanation

`lim _{x=c} f(x)=lim _{x=c} cos (x)`


Put `x=h+c`


And as mentioned above, when `{x} Rightarrow {c}` then it means that `{h} Rightarrow 0`


Which gives us `lim _{h=0} cos (c+h)`


Expanding `cos (h+c)=cos (h) cos (c)-sin (h) sin (c)`


Which gives us `lim _{{h}=0} cos ({h}) cos ({c})-sin ({h}) sin ({c})`



`=cos (c) cos (0)-sin (c) sin (0) `


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