I don't understand what went wrong:

Evaluate the limit:
$$\lim_{x\rightarrow 0}\frac{8\sin^2(x)}{1-\cos(x)}$$
$$=&\lim_{x\rightarrow 0}\frac{8\sin^2(x)}{1-\cos(x)}$$ \\
$$=&\lim_{x\rightarrow0}\frac{8\sin^2(x)}{1-\cos(x)}\times\frac{1+\cos(x)}{1+\cos(x)}$$ \\
$$=&\lim_{x\rightarrow 0}\frac{4\sin^2(x)(1+\cos(x))}{1-\cos^2(x)}$$ \\
$$=&\lim_{x\rightarrow 0}\frac{4\sin^2(x)(1+\cos(x))}{\sin^2(x)}$$ \\
$$=&\lim_{x\rightarrow 0}4(1+\cos(x))$$ \\
$$=&4(1+\cos(0))$$ \\
$$=&4(1+1)=8$$ \\

And it prints out aligned but with weird text all the way on the right side.

Thank you so much

  • $$...$$ is deprecated anyway, but definitely wrong inside of align* -- just omit it, you're using 'display math' already with align*
    – user31729
    Dec 14 '17 at 1:23

Your problem are the $$ in the align section. Also, your code is not complete/compilable. But, I think you want something like this.

Evaluate the limit:
\[ \lim_{x\rightarrow 0}\frac{8\sin^2(x)}{1-\cos(x)} \]
&=\lim_{x\rightarrow 0}\frac{8\sin^2(x)}{1-\cos(x)} \\
&=\lim_{x\rightarrow0}\frac{8\sin^2(x)}{1-\cos(x)}\times\frac{1+\cos(x)}{1+\cos(x)} \\
&=\lim_{x\rightarrow 0}\frac{4\sin^2(x)(1+\cos(x))}{1-\cos^2(x)} \\
&=\lim_{x\rightarrow 0}\frac{4\sin^2(x)(1+\cos(x))}{\sin^2(x)} \\
&=\lim_{x\rightarrow 0}4(1+\cos(x)) \\
&=4(1+\cos(0)) \\
&=4(1+1)=8 \\

enter image description here

  • 2
    Replace $$...$$ by \[...\] and I might upvote :-)
    – campa
    Dec 14 '17 at 11:51
  • Thank you very much. It was only part of my document but it is fixed now. Thank you.
    – RJ Yarwood
    Dec 14 '17 at 17:12

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