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shahzadjalbani Group Title

{sin7x/sin6x x not = 0 f(x)={6/7 x=0 is function continuous

  • 2 years ago
  • 2 years ago

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  1. shahzadjalbani Group Title
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    @physicsme @shadowfiend @anuragtripathi @daniellemmcqueen @LivForMusic @karatechopper

    • 2 years ago
  2. physicsme Group Title
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    @ujjwal

    • 2 years ago
  3. shahzadjalbani Group Title
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    @ujjwal

    • 2 years ago
  4. physicsme Group Title
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    @supercrazy92

    • 2 years ago
  5. ujjwal Group Title
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    Is the question demanding if the function continuous at 0 or not?

    • 2 years ago
  6. shahzadjalbani Group Title
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    Is function is continuous......? @ujjwal

    • 2 years ago
  7. ujjwal Group Title
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    do you know they define continuity at a point? Here the question should be, "is the function continuous at x=0?"

    • 2 years ago
  8. shahzadjalbani Group Title
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    yes this is the question.... @ujjwal

    • 2 years ago
  9. ujjwal Group Title
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    To test the continuity of function at x=0, find the limit when x--->0 And the find f(0). If \[\\lim_{x \to 0}f(x)=f(0)\] the the function is continuous at x=0

    • 2 years ago
  10. ujjwal Group Title
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    X tends to 0 when x is not equal to 0

    • 2 years ago
  11. joemath314159 Group Title
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    Lets re-write the function:\[\frac{\sin(7x)}{\sin(6x)}=\frac{\frac{\sin(7x)}{7x}}{\frac{\sin(6x)}{7x}}\]Now multiply the numerator and denominator by 7/6:\[\frac{\frac{7}{6}\cdot \frac{\sin(7x)}{7x}}{\frac{7}{6}\cdot \frac{\sin(6x)}{7x}}=\frac{\frac{7}{6}\cdot \frac{\sin(7x)}{7x}}{\frac{\sin(6x)}{6x}}\]Now you can take the limit as x goes to 0 using the fact that:

    • 2 years ago
  12. joemath314159 Group Title
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    \[\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1\]

    • 2 years ago
  13. joemath314159 Group Title
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    sry, pressed post before i was done.

    • 2 years ago
  14. ujjwal Group Title
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    \[\lim_{x \to 0}f(x)=\lim_{x \to 0}\frac{\sin 7x}{\sin 6x}\]\[=\lim_{x \to 0}\frac{\frac{\sin 7x}{7x}}{\frac{\sin 6x}{6x}}\times \frac{6}{7}\]\[=\frac{6}{7}\] Also, f(0)=6/7 since\[\lim_{x \to 0}f(x)=f(0)\]The function is continuous at x=0

    • 2 years ago
  15. ujjwal Group Title
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    It is already mentioned above but then i would like to post it again. \[\lim_{x \to 0}\frac{\sin \theta}{\theta}=1\]

    • 2 years ago
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