find the value of a and b when
lim x→0 [x(1-acosФ) - bsinФ]/x³ = 1 ??????????????
Answers
Answer:
Because
x
=
−
1
is a zero of
x
3
+
1
, we can be certain that
x
−
(
−
1
)
(that is:
x
+
1
) is a factor of
x
3
+
1
lim
x
→
−
1
x
3
+
1
x
2
−
1
=
lim
x
→
−
1
(
x
+
1
)
(
x
2
−
x
+
1
)
(
x
+
1
)
(
x
−
1
)
=
lim
x
→
−
1
x
2
−
x
+
1
x
−
1
=
(
−
1
)
2
−
(
−
1
)
+
1
(
−
1
)
−
1
=
1
+
1
+
1
−
2
=
−
3
2
If you haven't memorized how to factor the sum (and difference) of two cubes, use polynomial division to factor. If you don't know how to do polynomial division, you'll need to think it through.
x
3
+
1
=
(
x
+
1
)
(
something
)
Since we want the product to start with
x
3
, the
something
must start with
x
2
.
x
3
+
1
=
(
x
+
1
)
(
x
2
+
other stuff
)
But now when we distribute the
+
1
, we get an
x
2
which does not appear in the product.
We cat fix this by putting in a
−
x
at the beginning of the
other stuff
x
3
+
1
=
(
x
+
1
)
(
x
2
−
x
+
??
)
We know we want to end with
+
1
, so let's put a
+
1
in.
(
x
+
1
)
(
x
2
−
x
+
1
)
.
Multiply it out and we get
x
3
+
1
Step-by-step explanation: