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

Video Answer:

Solved by verified expert

Pritesh Ranjan

Other Schools

Best Match Question:

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

Discussion

You must be signed in to discuss.

Video Transcript

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.

Did you know?

Numerade has step-by-step video solutions, matched directly to more than +2,000 textbooks.