Asked by Anonymous
Definition of Derivative Question
lim as h approaches 0
square root of (16+h) - 4 / h
lim as h approaches 0
square root of (16+h) - 4 / h
Answers
Answered by
Reiny
Lim (√(16+h) - 4)/h as h --> 0
= Lim (√(16+h) - 4)/h * (√(16+h) + 4)/(√(16+h + 4)
= Lim (16+h - 16) / (h(√(16+h) + 4)
= lim 1/(√(16+h + 4)
= 1/(√16 + 4) = 1/8
= Lim (√(16+h) - 4)/h * (√(16+h) + 4)/(√(16+h + 4)
= Lim (16+h - 16) / (h(√(16+h) + 4)
= lim 1/(√(16+h + 4)
= 1/(√16 + 4) = 1/8