How to solve 3x+sinx=ex

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manpreet Tuteehub forum best answer Best Answer 3 years ago

How doese one solve this equation?

 

3x+sinx=ex3x+sin⁡x=ex

 

I tried graphing it and could only find approximate solutions, not the exact solutions. My friends said to use Newton-Raphson, Lagrange interpolation, etc., but I don't know what these are as they are much beyond the high school syllab

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manpreet 3 years ago

A nice method to find an approximate solution is to successively cut intervals in half, as follows: let's first rewrite this as

f(x)=3x+sinxex=0f(x)=3x+sin⁡x−ex=0
Now pick two values, aa and bb, such that f(a)<0f(a)<0 and f(b)>0f(b)>0. (You might have to make a few guesses before finding such values!) In this case, let's choose a=0a=0 and b=1b=1:
f(a)=3(0)+sin(0)e0=1<0f(a)=3(0)+sin⁡(0)−e0=−1<0
f(b)=3(1)+sin(1)e1=1.12...>0f(b)=3(1)+sin⁡(1)−e1=1.12...>0

 

Now, because our function 

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