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Find the value of Limit Below sin 7x cot 4x lim X-0 x cot 3x

in this problem we have to figure out the limit of This given function as x tends to zero. So as we know that according to an expression and identity limit of sine X by X when X tends to zero, that is basically one. So we will use this idea and Using this idea let's multiply 7 to the numerator and denominator. So it turns out to be seven sign seven X by seven X. And now we can observe that Limit of Science seven x by seven X. That will be one. So this can be eliminated and we can just write limit X tends to zero seven times one that will be seven. So we will just leave it as it is caught for X by caught three X. And now let's just change this a bit. Let's write caught in terms of cars and signs. So we get this as limit X tends to 07 times cost for X by sign for X divided by Cost three X over sign three X. And this turns out to be limited, extends to zero seven times costs for X into sine three X over Cost three x into sine for X. And now we observed that let's divide by for X and multiply forex here, similarly in the numerator let's divide it with three X. And multiply three X. And now we observed that limit of sign three X by three X. And limit of sign for X by forex that will be one. So this improves as limit X tends to zero seven times costs for x By cost three x into three X by four X. That will be just three by four. And now we can put the value of X is zero because it turns out to be a determinant value and costs a four X or cost of three X as X tends to zero, that's going to be one. So the answer will be seven times three by four and this turns out to be 21 by four.

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