lim f(5 + h) − f(5)/h(adsbygoogle = window.adsbygoogle || []).push({});

h→0

given that f(5) = 4 and f (5) = −95.

Iam not really sure how to approach this problem. I know its in 0/0 form so you can use L'hosp rules.

For another question Iam asked to find the equation for the tangent line of

xy 3 + y − 23 = x

where y = 2.

is this a related rates problem?? Did I approach this right:

(x)(3y^2 dy/dx) + (y^3)(1) + 1 dy/dx = 1

= 3y^2 dy/dx + 1 dy/dx = 1 - y^3

= (dy/dx) 3y^2x + 1) = 1 - y^3

dy/dx = (1-y^3)/(3y^2x + 1)

then x = 3 from original equation.

dy/dx = -7/12(3)+1

= -7/37

then

Tangent line = y = mx + b

y = -7/37(3) + 2??

Thanks for your help

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# How to approach problems on limits

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