Evaluate the limit #lim_(h rarr 0) (1-cosh)/h^2# numerically ?

Answer 1

You cannot "prove" that a limit exists numerically but we can examine its general behaviour. The easiest way is to use a spreadsheet:

Define a function:

# F(h) = (1-cos h)/h^2 #

Then we tabulate the function using and initial value of #h=1#and bisect the interval during each calculation:

As we can see with #h = 0.00000763# we have #f(h)=0.50000000#, but there still could be some odd behaviour or a discontinuity that we are unaware of in the interval:

# 0 lt h lt 0.00000763 #

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Answer 2

The limit lim_(h rarr 0) (1-cosh)/h^2 numerically evaluates to approximately -0.5.

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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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