 On this bridge a man is standing on the bridge and just below the man 3 meters down is the position of the boat. Now the boat starts moving at a speed of 5 meters per minute. Going along the bridge at a speed of 4 meters per minute. So basically the situation is wherever I am standing and the boat is here. The boat starts moving this way and the man starts walking this way. And perpendicular to the bridge the boat starts moving. Now find the change or find the rate of separation and the boat. The instant when time is 4 minutes assuming t equal to 0 is when they just started moving. So simultaneously man starts walking on the bridge and boat starts moving perpendicular to the bridge. So after exactly at t equal to 4 minutes what is the rate of separation of... The boat is moving this way and the man is moving this way. Any question with this picture? So the man is standing and the boat is moving this way and the man is moving this way. So how much? So the change in the separation is what we are concerned. So this is bringing minus x2 whole square which is 16 t square. Y1 minus Y2 whole square which is 25 t square at the instant t is 4. Let's differentiate this. So this will be 1 by 2. So this is 41 t square. So 41 t square plus 9 into 82. Now substitute t as... So basically this will become 41 so it becomes 164 by 16. How much is 41 into 16? 656 plus 9 is 665. So answer is 164 by root 665 meters per minute. Question Vishak? Passion? Just to find of x. There is a change in the value of x by delta x. So we normally call delta x as the absolute term switch which you should be knowing. If I say delta x by x this is called the relative because this was a chapter in physics. Output will also change without approximation very first. So let's say I give an example to start with. Let's say the edge 2 centimeter. So you know the 8 centimeter. It was 36 centimeter. It was 36 cube. That will be used fast. Of course you do not want to spend too much time on it. So what slight change will you make in your answer so that you are almost close to the volume of the new edge. So that is what we need adjustments to get an optimum benefit from this method. Listen to this sometimes it is very useful in doing your chemistry calculations also. Now from here if I want to know how much adjustment should I make in y. Can I say I can just send the y on the other side. The y here is f of x so both sides. That means your error should be very very small. So when you do the comes f dash x by first principles. So we say delta y by delta x this is tending to 0 px calculate x where the error has occurred. This is important. So you need to know 36. So how should I at least if I know this I will add it to 8 to get my answer. So what you do x is not exactly tending to 0. So you can say it is approximately deeply so much. If you take it to on the other side it will be 0.0036 dx. 3x square putting x as 2x. So what will it be 36 is 12. So that means delta v is 12 times 0.0036. How much is 36 into 12? 72. 36 so 43 correct. So you knew which is 8 plus 0.0432 which is 8.0432 centimeter cube. So I never sat into 0.0036 whole cube. I just saw how much adjustment I have to make to my volume. Or what is the error it will request you to take out your calculator if you haven't just checked. If I do just 2.0036 whole cube how close am I to the answer? Very close. How much is the answer? 3.043277. See it's almost very close right. As the error of this delta v is always x plus delta x. So you can take it externally. Do not assign any sign randomly to the delta x or delta y thing. Let's take a question. Let's take a question in approximate value. This is delta x. It was 125 what would have been y. And now it is 127 what is my error in the y and add it to y. 0.667 0.167 okay let's check. Okay first of all this is possible. So find such an x whose cube root 125 which is a perfect which clearly implies the absolute error 0.0 It's actually a 1 right. If you want to be very close to 4 to 7 places you can say 0.2667 Okay the error in the y is 0.02667 So the new value which is what I desired So the new value will be the previous value as this correction that you need So just use your calculator and check whether actually calculating it you can solve your problem in this method. Your question of values 40 cube root that value will be struggling. That's how it will not be answered. Those questions will not be answered.