Help Please. Question: For the function f(x)=2x+3 evaluate lim /\x>0, f(x+/\x)-f(x) / /\x algebraically.
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jqueener21
ANSWERS: 1
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The trick about taking the differential limit is properly evaluating the limit variable within the function so that the limit variable in the denominator disappears. My prefered variable is "h". I like it because it tends to "standout" in the expression so that you can better see how to eliminate it from the denominator. Using "h" as the limit variable, the differential limit notation becomes: lim [f(x+h) - f(x)]/h h→0 In your case, f(x) = 2x + 3 Therefore, f(x+h) = 2(x + h) + 3 You can now simplify f(x + h) by using the distributive property a(b + c) = ab + ac, and then subtract f(x) from the simplified expression. If you do this correctly, the "h" will quickly divide into the numerator; thereby, allowing you to safely take the limit.
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