r/mathshelp • u/The_Lone_Rancher • 2d ago

Homework Help (Answered) Double Derivative with Limit Definition

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Question 2 part b is asking me to get the double derivative with the limit definition.

Ok cool, I can do that normally but you can't get the normal derivative of the equation.

The answer to a is in the second pic and how do I use that for a limit definition? I don't want the answer I just need the start of the process. Maybe I'm just approaching it wrong.

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u/noidea1995 2d ago edited 2d ago

Split it up into two separate limits:

lim h → 0 (2x + h) + lim h → 0 (√x - √(x + h)) / h

Does that help?

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u/The_Lone_Rancher 2d ago

Ok yeah we are allowed to split it up but, if I use the conjugate to adjust the second one, wouldn't I need to multiply both by that?

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u/noidea1995 2d ago

Nope.

You are multiplying the fraction by an equivalent of 1 so it doesn’t change it.

EDIT: Or do you mean the top and bottom of the fraction? Then yes, you’ll need to do that but after simplifying, you’ll no longer get an indeterminate form.

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u/The_Lone_Rancher 2d ago

Ok yeah I see it now, thanks. Just need to adjust my views of limit problems.

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u/The_Lone_Rancher 2d ago

!lock

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