I would like help to find a polynomial.
the question says the function F(x) = tan(x) where
x in radians is to be approximated in the interval [0.2,1] to the polynomial p(x) = ax +bx^3 +cx^5
write down three linear equations when the polynomial is exact at the points x = 0.2, 0.7, 1

Question

I would like help to find a polynomial.
the question says the function F(x) = tan(x) where
x in radians is to be approximated in the interval [0.2,1] to the polynomial p(x) = ax +bx^3 +cx^5
write down three linear equations when the polynomial is exact at the points x = 0.2, 0.7, 1

anonymous · Answer

Write three equations as
$$
\tan (u) = a u + b u^3 + c u^5\
\text { for }  u=.2, .7, 1

$$

anonymous · Answer

$$
0.20271=0.2 a+0.008 b+0.00032 c \

0.842288=0.7 a+0.343 b+0.16807 c\

1.55741= a+ b +c

$$

anonymous · Answer

If you solve them, you get
$$

a = 1.00226,\ b = 0.270994,\
 c = 0.284158
$$

anonymous · Answer

thank you for this answer, where I was going wrong was for some reason I was ignoring tan(x). I couldn't see the woods for the tree,s jk67

anonymous · Answer

yw