Show that, for small values of x, the graph of
y = 5 + 4 \\sin \left( \frac{x}{2} \right) + 12 \tan \left( \frac{x}{3} \right)
can be approximated by a straight line. - AQA - A-Level Maths Mechanics - Question 5 - 2018 - Paper 3
Question 5
Show that, for small values of x, the graph of
y = 5 + 4 \\sin \left( \frac{x}{2} \right) + 12 \tan \left( \frac{x}{3} \right)
can be approximated by a straight li... show full transcript
Worked Solution & Example Answer:Show that, for small values of x, the graph of
y = 5 + 4 \\sin \left( \frac{x}{2} \right) + 12 \tan \left( \frac{x}{3} \right)
can be approximated by a straight line. - AQA - A-Level Maths Mechanics - Question 5 - 2018 - Paper 3
Step 1
Use small angle approximation for sin x or tan x
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Answer
For small values of x, we can use the approximations:
Conclude that the graph can be approximated by a straight line
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Answer
The resulting equation is:
[ y = 6x + 5 ]
This represents a straight line with a slope of 6 and a y-intercept of 5. Therefore, we can conclude that for small values of x, the graph can indeed be approximated by a straight line.
