Answer:
y(-4) = 5
y'(-4) = -7
Step-by-step explanation:
Hi!
Since the tangent line T and the curve y must coincide at x=-4
y(-4) = T(-4) = 5
On the other hand, the derivative of the curve evaluated at -4 y'(x=-4) must be the slope of the tangent line. Which inspecting the tangent line T(x) is -7
That is:
y'(-4) = -7
Answer:
see explanation
Step-by-step explanation:
Under a rotation about the origin of 90°
a point (x, y ) → (- y, x ), thus
A(2, 2 ) → A'(- 2, 2 )
B(2, 4 ) → B'(- 4, 2 )
C(4, 6 ) → C'(- 6, 4 )
D(6, 4 ) → D'(- 4, 6 )
E(6, 2 ) → E'(- 2, 6 )
Answer:

The polynomial is an approximation with an error less than or equals to <em>0.002652</em> for x in the interval
[-1.113826815, 1.113826815]
Step-by-step explanation:
According to Taylor's theorem
with
for some c in the interval (-x, x)
In the particular case f
<em>f(x)=cos(x)
</em>
<em>
</em>
we have
therefore
and the polynomial approximation of T5(x) of cos(x) would be
In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that
for some c in (-x,x). So
and we must find the values of x for which
Working this inequality out, we find
Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval
[-1.113826815, 1.113826815]