# How do you find the limit of #(sqrt(49+h)-7)/h# as h approaches 0?

How: Rationalize the numerator,

(I assume that you have recently begun your study of calculus and do not yet have access to l'Hopital's rule, which is not needed in this problem anyway.)

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To find the limit of (sqrt(49+h)-7)/h as h approaches 0, we can use the concept of limits and algebraic manipulation.

First, let's simplify the expression by rationalizing the numerator.

Multiply both the numerator and denominator by the conjugate of the numerator, which is sqrt(49+h) + 7.

This gives us [(sqrt(49+h) - 7)(sqrt(49+h) + 7)] / (h * (sqrt(49+h) + 7)).

Expanding the numerator using the difference of squares, we get (49+h - 49) / (h * (sqrt(49+h) + 7)).

Simplifying further, we have h / (h * (sqrt(49+h) + 7)).

Now, cancel out the h terms in the numerator and denominator, leaving us with 1 / (sqrt(49+h) + 7).

As h approaches 0, the expression becomes 1 / (sqrt(49+0) + 7), which simplifies to 1 / (7 + 7).

Therefore, the limit of (sqrt(49+h)-7)/h as h approaches 0 is 1/14.

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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.

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