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How do you solve #e^x-9xe^x=0#?

Answer 1

Serenity Johnson

Factor and solve each factor equal to #0#

#e^x-9xe^x=0#

#e^x(1-9x) = 0#

#e^x = 0# #" "# or #" "# #1-9x =0#

#e^x# is never #0#

#1-9x =0# when # = =1/9#

The only solution is #1/9#

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Answer 2

Greyson Brown

To solve the equation ( e^x - 9xe^x = 0 ), you can factor out the common term ( e^x ) and then solve for ( x ).

First, factor out ( e^x ) from the equation: [ e^x(1 - 9x) = 0 ]

Now, set each factor equal to zero and solve for ( x ): [ e^x = 0 ] This equation has no real solutions since ( e^x ) is always positive.

[ 1 - 9x = 0 ] Solve for ( x ): [ 9x = 1 ] [ x = \frac{1}{9} ]

Therefore, the solution to the equation ( e^x - 9xe^x = 0 ) is ( x = \frac{1}{9} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.