Question

Let y=3x^2.

Find the change in y, Δy when x=4x and Δx=0.2

Find the differential dy when x=4x and dx=0.2

Answer 1

1. 
   Anu 3 X x-4 amd bx-os in the above equation oy = 9.93
   
   0 4O
   please like

Answer 2

Let $y=2\sqrt{x}$. 
Find the change in $y$, $\Delta y$ when $x=4$ and $\Delta x=0.2$

Answer 3

Our first order of business here is to find the derivative of the equation (i.e. differential equation). This requires u-substitution...

 

u = 5x + 6

du = 5 dx

 

Now to the equation...

 

y = tan u

dy = sec²u * du

     = sec²(5x+6)*5dx

 

So now we have our differential equation. Onward...

 

Solve for dy when x = 4 and dx = 0.4...

 

dy = sec²(5*4 + 6)*5*0.4

dy = sec²(26) * 2

dy = 2.38946 * 2

dy = 4.77892

 

Yay! The second case is solved the same way. :)