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daniel1480
28.09.2019 •
Mathematics
The equation e^(4x) + x=2 has a solution near x=0. by replacing the left side of the equation by its linearization, find an approximate value for the solution.
**write the exact answer**
x=
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Ответ:
Using the linearization mehod, find f'(x) if f(x)=e^(4x)+x, f(x) is approximately =mx+b where m=f'(0). We want to know the value of the x and y intercepts, so we substitute them with 0(vice versa), we will get (0,f(0))=(0,1)
Solve for x:
f'(x)=(4x)'e^(4x)+(x)'
(4x)'=4 (x)'=1
f'(x)= 5
solve for b:
e^0=1
1= 0+b
b=1
so the approximation for f(x) is y=5x+1
Solve for y, so you substitute the values of x and b
5x+1=2 -1 -1
5x=1 x=1/5
so exact answer is x= 0.2
Ответ:
160
Step-by-step explanation: