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What is the equation of the tangent line of #f(x) =sqrt(x-15)/x-1/2# at #x=31#?

Answer 1

Emma Aldridge

Equation of tangent is # x+ 7688 y = -2821#

# f(x) = sqrt (x-15)/x-1/2 ; x=31#

#:. f(31) = sqrt (31-15)/31-1/2=4/31-1/2=- 23/62#

Point is #(31,-23/62)# at which tangent was drawn.

# f(x) = sqrt (x-15)/x-1/2 ; #

# f^'(x) = ((x *1/(2 sqrt (x-15))- sqrt (x-15)*1))/x^2 #

Slope= #= f^'(31) = (31/8- 4)/31^2= -1/7688 #

Equation of tangent at #x=31# is #y+23/62= -1/7688(x-31)#

or # 7688 y +2852 = -x+31 #or

# x+ 7688 y = -2821#

Equation of tangent is # x+ 7688 y = -2821# [Ans]

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Answer 2

Scarlett Allison

The equation of the tangent line of f(x) = sqrt(x-15)/(x-1/2) at x=31 is y = -1/8x + 33/8.

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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.