Can you find the change?

Question

Let .

Find the change in ,  when  and  4.0Incorrect  

Find the differential  when  and 

Answer 1

y = 2√x

Then y₁ = 2√4 =4 and y₂ = 2√4.4 = 4.195235 . Hence Δy = y₂ - y₁ = .195235

Now dy / dx = 1 / √x ⇒ d y = d x / √x

Hence d y = 0.4 /√4 ⇒ d y = 0.2

Answer 2

Alright, let us tackle it;

First, we rewrite;

y=2x^1/2 (In derivation, we use exponents and not root.)

Now the change;

change in y = y(x + change in x) - y(x)

=2(x + change in x)^1/2 - 2(x)^1/2

=2(4 + 0.4)^1/2 - 2(4)^1/2

=0.1952

Solving the differential at the given point we first find the derivative...

dy=x^-1/2dx;

x = 4 ; dx = 0.4

dy=(4)^-1/2(0.4)

=0.4/√4 OR 2/(5√4) OR 1/5 OR 0.2.