anonymous
  • anonymous
am i solving this correctly? limx->0 sin 7x/4x
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\lim_{x \rightarrow 0} \frac{ \sin7x }{ 4x }\]
anonymous
  • anonymous
\[\lim_{x \rightarrow 0} \frac{ 4 }{ 7 }( \frac{ \sin x }{ x })\]
anonymous
  • anonymous
\[\frac{ 4 }{ 7 }\lim_{x \rightarrow 0} \frac{ \sin x }{ x }\]

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anonymous
  • anonymous
sin x/x is just 1 and 4/7 times 1 is just 4/7
anonymous
  • anonymous
done?
anonymous
  • anonymous
\[\lim_{x\to0}\frac{\sin ax}{ax}=1\] So, \[\lim_{x\to0}\frac{\sin7x}{4x}=\frac{7}{7}\lim_{x\to0}\frac{\sin7x}{4x}=\frac{7}{4}\lim_{x\to0}\frac{\sin 7x}{7x}=\cdots \]
anonymous
  • anonymous
The answer should be the reciprocal of what you got: 7/4.
anonymous
  • anonymous
haha yes, ofcourse, typo there. i meants 7/4
anonymous
  • anonymous
meant*
anonymous
  • anonymous
so
anonymous
  • anonymous
\[\lim_{x \rightarrow 0} \frac{ 7 }{ 4 }( \frac{ \sin x }{ x })\]
anonymous
  • anonymous
\[\frac{ 7 }{ 4 }\lim_{x \rightarrow 0} \frac{ \sin x }{ x }\]
anonymous
  • anonymous
= 7/4
anonymous
  • anonymous
No, multiply by 7/7 (=1) and then switch out the 4x for 7x, then the sin7x or 7x turns into one. 1 times 7/4 will be 7/4. You got the right answer, but in the wrong way.
anonymous
  • anonymous
you just switch.. ok then

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