Show that, for small values of x, the graph of
$y = 5 + 4 rac{ ext{sin} rac{x}{2}}{2} + 12 an rac{x}{3}$
can be approximated by a straight line. - AQA - A-Level Maths Pure - Question 5 - 2018 - Paper 3
Question 5
Show that, for small values of x, the graph of
$y = 5 + 4 rac{ ext{sin} rac{x}{2}}{2} + 12 an rac{x}{3}$
can be approximated by a straight line.
Worked Solution & Example Answer:Show that, for small values of x, the graph of
$y = 5 + 4 rac{ ext{sin} rac{x}{2}}{2} + 12 an rac{x}{3}$
can be approximated by a straight line. - AQA - A-Level Maths Pure - Question 5 - 2018 - Paper 3
Step 1
Use small angle approximation for sin x or tan x
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Sign up now to view full answer, or log in if you already have an account!
Answer
Substituting the approximations back into the equation gives us:
y = 5 + 4 rac{ rac{x}{2}}{2} + 12 rac{x}{3}
This simplifies to:
y = 5 + 4 rac{x}{4} + 4x
So,
y=5+x+4x=5+5x
Step 3
Conclude that the graph can be approximated by a straight line
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The equation we derived is:
y=5+5x
This is the equation of a straight line in the form y=mx+c where m=5 and c=5. Therefore, for small values of x, the graph of y can indeed be approximated by a straight line.
