 Hello and welcome to this session. In this session we discuss the final question that says evaluate limit x tends to 0, 1 plus 5x is held to the power of 2 upon x. Before we move on to the solution, let's discuss one special limit that we would use in the solution for this question which says that limit x tends to infinity 1 plus 1 upon x, this held to the power of x is equal to e. Now when we apply this limit, we have to make sure that this first term of the function should be 1 and the second term and the index should be reciprocal of each other. Also this index should approach to infinity then only this limit would be equal to e. This will be key that we use for this question. To proceed with the solution now, we are supposed to evaluate the limit x tends to 0, 1 plus 5x this hold to the power of 2 upon x, 5x to the power of the reciprocal of 5x which is 1 upon 5x. So this is equal to limit x tends to 0, 1 plus 5x this hold to the 5x to the power 1 upon 5x and this hold to the power of 1 upon 5x this is equal to limit 1 upon to infinity the hold to the power of 1 upon 5x and this hold to the power of. Now this result stated in the key idea according to which we have limit x tends to infinity 1 plus 1 upon x hold to the power of x is equal to e could be used for this the power of 1 upon 5x could be written as e and this e to the power of tends to 0, 1 plus 5x this hold to the power of 2 upon x is equal to e to the power of c session. Hope you understood the solution of this question.