The equation e^x +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
exact answer

Question

The equation e^x +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
exact answer

dumbcow · Answer

$$f(x) \approx f'(a) (x-a) + f(a)$$
when x is near a

anonymous · Answer

would i bring the 2 to the other side ?

dumbcow · Answer

no its not needed but you could and would still get same answer

anonymous · Answer

so i find the d/dx of e^x+x would be e^x+1 correct?
then f(a)= f(0)= e^x+x=0?
f*(a)= e^x+1=e^(0)+1 = 1?

dumbcow · Answer

not quite ..... e^0 = 1
anything to 0 power is 1

anonymous · Answer

so f(a)=1 
f*(a)=2?

dumbcow · Answer

yes

anonymous · Answer

2x+1 is what i got but they're asking for the exact value ?
so would i make it 2x+1=0?

dumbcow · Answer

no the "2x+1" replaces the "e^x + x" 

--> 2x+1 = 2

dumbcow · Answer

see how it approximates "e^x +x" close to 0 http://www.wolframalpha.com/input/?i=plot+%28e%5Ex+%2B+x%2C+2x%2B1%29+for+x+%3D+-1+to+1

anonymous · Answer

alright thanks