How do you evaluate the limit #(sqrt(x^2+7)-3)/(x+3)# as x approaches 3?
Since the function is not indeterminate when x = 3, we can evaluate the limit by direct substitution.
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To evaluate the limit (sqrt(x^2+7)-3)/(x+3) as x approaches 3, we can use algebraic manipulation and the concept of limits. By substituting x = 3 into the expression, we get an indeterminate form of 0/0. To resolve this, we can simplify the expression by multiplying the numerator and denominator by the conjugate of the numerator, which is sqrt(x^2+7) + 3. After simplification, we obtain the expression (x-3)/(x+3)*(sqrt(x^2+7) + 3). By substituting x = 3 into this simplified expression, we get 0/6, which equals 0. Therefore, the limit of (sqrt(x^2+7)-3)/(x+3) as x approaches 3 is 0.
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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.
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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