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

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

As we can see with

# 0 lt h lt 0.00000763 #

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

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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.

- What is the limit of #(x^2 + 2) / (x^3 + x^2 -1)# as x approaches negative infinity?
- How do you find the limit of #[1/e^(x +1)]^sqrtx # as x approaches 0?
- How do you evaluate the limit #tan(4x)/x# as x approaches #0#?
- How do you find the limit of #sqrt(x+1)# as #x->3#?
- How do you find the limit of #(4x^2 -3x+2)/(7x^2 +2x-1)# as x approaches infinity?

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