What is the equation of the tangent line of # f(x)=1/x+1 # at # x=2 #?

Answer 1

#y=-1/4x+2#

We need to know m, its gradient, and a point in order to find the equation of the tangent. f'(2) will provide the value of m, and evaluating f(2) will result in a point on the line.

express #f(x)=1/x+1=x^-1+1#
#rArrf'(x)=-x^-2=-1/x^2#
#rArrf'(2)=-1/(2)^2=-1/4=m#
and #f(2)=1/2+1=3/2rArr(2,3/2)" is a point on tangent line"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(y-b=m(x-a))color(white)(a/a)|)))# is the equation of line where m is gradient and (a ,b) a point.
using #m=-1/4" and " (a,b)=(2,3/2)#
#y-3/2=-1/4(x-2)#
#rArry=-1/4x+2" is equation of tangent line at x = 2"# graph{(y-1/x-1)(y+1/4x-2)=0 [-10, 10, -5, 5]}
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Answer 2

The equation of the tangent line of f(x)=1/x+1 at x=2 is y = -1/4x + 3/2.

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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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