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f(x) = 3x² Obtain $$ ext{lim}_{h o 0} \frac{f(x + h) - f(x)}{h}$$ Circle your answer. - AQA - A-Level Maths Pure - Question 3 - 2021 - Paper 3
Question 3
f(x) = 3x² Obtain $$ ext{lim}_{h o 0} \frac{f(x + h) - f(x)}{h}$$ Circle your answer.
Worked Solution & Example Answer:f(x) = 3x² Obtain $$ ext{lim}_{h o 0} \frac{f(x + h) - f(x)}{h}$$ Circle your answer. - AQA - A-Level Maths Pure - Question 3 - 2021 - Paper 3
Step 1
Obtain $$\text{lim}_{h \to 0} \frac{f(x + h) - f(x)}{h}$$
Answer
To find the limit, we first need to calculate (f(x + h)):
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Substitute (x + h) into the function: [f(x + h) = 3(x + h)^2 = 3(x^2 + 2xh + h^2) = 3x^2 + 6xh + 3h^2]
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Now, calculate (f(x + h) - f(x)): [f(x + h) - f(x) = (3x^2 + 6xh + 3h^2) - 3x^2 = 6xh + 3h^2]
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Substitute this result into the limit expression: [\frac{f(x+h) - f(x)}{h} = \frac{6xh + 3h^2}{h} = 6x + 3h]
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Take the limit as (h) approaches 0: [\text{lim}_{h \to 0} (6x + 3h) = 6x]
Thus, the final answer is (6x).