# Use newtons method to approximate a root of the equation e^(-x) = 5 + x correct to eight decimal places.

Question
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Use newtons method to approximate a root of the equation e^(-x) = 5 + x correct to eight decimal places.

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Step 1

Use newtons method to approximate a root of the equation e(-x) = 5 + x correct to eight decimal places.

Step 2

Consider the equation

e-x=5+x help_outlineImage TranscriptioncloseRewrite the aquation -5-x-0 Differanticate the fiunction by xaz follows f'(x)= --1 equate f'(x)=0 --1-0 xine-In(-1) x-3.14 choose the irnitial value as follows x15 By Newton's method f(x.) f (x,) f'(%) 1.5--15) f(-1.5) f(-1.5)-0.981689070 f(-1.5)--5.418689070 Therefore 0.981689070 x--15- (-5.481689070) --1.320914857 fullscreen
Step 3

At n=1

... help_outlineImage TranscriptioncloseBy Newton's method f(x,) 2 f'(x) f(-1.320914857) f'(-1.320914857) =-1.320914857 f(-1.320914857) = 0.067762497 f'(-1.320914857) = -4.746847640 Therefore, 0.067762497 x -1.320914857 - (-4.746847640) -1.306639594 fullscreen

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### Calculus 