Use the definition of continuity and the properties of limits to show that the function h(x)=x+3/(x2-x-1)(x2+1) is continuous at x = -2.
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We are asked to use the property of limit and continuity to show that the function h(x) is continuous at x= -2.

The function h(x) is given by:

since clearly as we know that Polynomial functions are continuous everywhere so, the term in the numerator is continuous at x= -2.

Also the term in the denominator is continuous at x= -2.

and the function h(x) is defined in the neighbourhood of x= -2 since the denominator is not equal to zero at x= -2.

Also at x= -2 ; the limit of the function h(x) exist .

The limit is given by:

Hence, the function is continuous at x= -2.

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step-by-step explanation:

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