# How do you find the limit of #sqrt(2-x^2)/x# as #x->0^+#?

then we can see that:

Which proves that:

graph{sqrt(2-x^2)/x [-10, 10, -5, 5]}

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To find the limit of sqrt(2-x^2)/x as x approaches 0 from the positive side, we can simplify the expression. By factoring out an x from the denominator, we get x * sqrt(2-x^2)/x. Canceling out the x terms, we are left with sqrt(2-x^2).

Now, as x approaches 0 from the positive side, the value of x^2 becomes very close to 0. Therefore, 2-x^2 approaches 2. Taking the square root of 2, we get sqrt(2).

Hence, the limit of sqrt(2-x^2)/x as x approaches 0 from the positive side is sqrt(2).

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