Find limit?
Find (in terms of the constant aa)
#lim_(h→0)(√4(a+h) - √4a )/ h#
Limit =
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Find (in terms of the constant aa)
Limit =
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2 Answers
Explanation:
Explanation:
Corrected from previous edition.
You already have half of the work completed by plugging f(x) into the difference quotient.
We have a domain restriction that we need to find a way to algebraically manipulate out of our function. We can't plug 0 into the denominator, so let's find a way to get rid of it.
The next step would be to multiply the top and bottom by the conjugate to clear the square root functions in the numerator.
Next, we simplify the functions by combining like terms in the numerator. Don't worry about the denominator, in most cases you will leave it in factored form.
In this case, our 4a and -4a will sum to zero and we will be left with h in the numerator
Our h factor will divide out of the numerator and denominator and we will be left with the following.
Now that our domain restriction has been removed, we can proceed with the direct substitution portion of the limit. Sub-in 0 for h and evaluate.
What we're left with is: