 Hello and how are you all today? The question says find limit x approaches 0 fx and limit x approaches 1 fx where fx is given to us as 2x plus 3 when x is less than equal to 0 and 3 bracket x plus 1 bracket close when x is greater than 0. Let us proceed on with our solution. Now we have to find out two values of fx. Firstly when limit x approaches to 0 from left inside fx and then when limit x approaches to 0 from right inside. Now let us substitute the values. We have to take the function as 2x plus 3 when x is less than equal to 0. So here we have the function as 2x plus 3 and we need to take the function as 3 bracket x plus 1 bracket close when x is greater than 0. So here the x is greater than 0. So we have limit x approaches to 0 from right inside 3 bracket x plus 1 bracket close. Now let us proceed on with these two functions one by one. Now here putting equal to 0 minus h we have as x approaches to 0 therefore h will also approach to 0. So we have limit h approaches approaching to 0 to bracket x that is 0 minus h plus 3. Further it is equal to limit h approaches to 0 minus 2h plus 3. Now in simply putting the value of h as 0 we have 0 plus 3 that is equal to 3. Now in the same way we will be solving out for the next one which is given to us. Here we will put x equal to 0 plus h. So as x approaches to 0 therefore h will also approach to 0. Now we have limit h approaches to 0 3 in the bracket in the place of x we have 0 plus h plus 1. Opening the brackets we have limit h approaches to 0 3 h plus 1. And on simply putting the value of h as 0 we have 3 in the bracket 0 plus 1 that is further equal to 3. So now we have that therefore limit x approaches to 0 from the left hand side the function is equal to limit x approaches to 0 from right hand side of the effig. The value of both are equal to 3. Now as x approaches 1 we have limit x approaching 1 effig. Now here the function will be equal to 3x plus 1 because we need to take this function where the value of x is greater than 0. So we have limit the value of the function when we take the value of x as 1 3 1 plus 1 which is equal to 3 into 2 that is further equal to 6. And the answer to the session is 3 comma 6. Right this ends my session hope you understood the concept well have a very nice day ahead.