 welcome to the session. My name is Kanika and I'm going to help you to solve the following question. The question says evaluate the following limits in exercises 1 to 22, limit of sine a x by sine b x as x tends to 0 where a and b are not equal to 0. Before solving this question we should know that limit of sine x by x as x tends to 0 is 1. The knowledge of this result is the key idea in this question. Let's now begin with the solution. In this question we have to evaluate limit sine a x by sine b x as x tends to 0. We will use this result to solve this question. So now multiply and divide sine a x by a x and multiply and divide sine b x by b x. Now this is equal to limit a x tends to 0 sine a x by a x because x tends to 0 implies a x also tends to 0 into a by b into limit b x tends to 0 b x by sine b x because x tends to 0 implies b x also tends to 0. Now this is equal to limit y tends to 0 sine y pi y where y is equal to a x into a by b into limit t tends to 0 t by sine t where t is equal to b x. Now the key idea we know that limit x tends to 0 sine x by x is 1. So this means limit sine y by y as y tends to 0 is also 1. So we have 1 into a by b into. Now this can be written as 1 by sine t by t and we know that limit of sine t by t as t tends to 0 is also 1. So limit of this is also equal to 1. So this is equal to a by b. Hence our required answer is a by b. So this completes the session. Bye and take care.