What is the equation of the line that is normal to #f(x)=-e^x # at # x=-2 #?

Answer 1

#xe^4-ye^2+2e^4-1=0#.

Let us recall that, #f'(x)# is the slope of tgt. to the curve # C : y=f(x)# at any pt. #(x,y)#.
For, #f(x)=-e^x, f'(x)=-e^x rArr f'(-2)=-e^-2=-1/e^2#.
#:.# the slope of tgt. to #C# at #x=-2# is #-1/e^2#, &, since, normal is
#bot# to tgt., the slope normal at #x=-2# will be #-1/(-1/e^2)=e^2#
Also, #x=-2 rArr f(-2)=-e^-2=-1/e^2#, so, the pt. of contact is #(-2,-1/e^2)#
Altogether, the normal passes thro. pt. #(-2,-1/e^2)# and has slope
#=e^2#. This gives us the eqn. of normal as # : y+1/e^2=e^2(x+2)#,
or, #ye^2+1=xe^4+2e^4, i.e., xe^4-ye^2+2e^4-1=0#.
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Answer 2

The equation of the line that is normal to f(x) = -e^x at x = -2 is y = 0.1353x + 0.2707.

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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.

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.

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.

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.

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