Answer:
The answers are 0, 1 and −2.
Step-by-step explanation:
Let α=arctan(2tan2x) and β=arcsin(3sin2x5+4cos2x).
sinβ2tanβ21+tan2β2tanβ21+tan2β23tanxtan2β2−(9+tan2x)tanβ2+3tanx(3tanβ2−tanx)(tanβ2tanx−3)tanβ2=3sin2x5+4cos2x=3(2tanx1+tan2x)5+4(1−tan2x1+tan2x)=3tanx9+tan2x=0=0=13tanxor3tanx
Note that x=α−12β.
tanx=tan(α−12β)=tanα−tanβ21+tanαtanβ2=2tan2x−13tanx1+2tan2x(13tanx)or2tan2x−3tanx1+2tan2x(3tanx)=tanx(6tanx−1)3+2tan3xor2tan3x−3tanx(1+6tanx)
So we have tanx=0, tan3x−3tanx+2=0 or 4tan3x+tan2x+3=0.
Solving, we have tanx=0, 1, −1 or −2.
Note that −1 should be rejected.
tanx=−1 is corresponding to tanβ2=3tanx. So tanβ2=−3, which is impossible as β∈[−π2,π2].
The answers are 0, 1 and −2.
4t ^ 2 - 16 ÷8 ÷ t - 2 ÷6
=(4t ^ 2)-(16 ÷8 ÷ t)-(2 ÷6)
=(4t ^ 2)-(2/t)-1/3
=4t ^ 2-2/t-1/3
Answer:
Last option: increasing: -2 < x < 0 and x> 3/2;
decreasing: x < -2 and 0 < x < 3/2
Step-by-step explanation:
The function given is an absolute cubic function. (Pictured below).
We can determine from the graph that the equation increases over the interval:
increasing: -2 < x < 0 and x> 3/2;
decreasing: x < -2 and 0 < x < 3/2
Answer:
(2 x +1) ( x + 1) = 2 x² + 3 x + 1
Step-by-step explanation:
The steops used to find the product of (2 x + 1) (x + 1) are
=( 2 x )× x + (2 x) × 1 + x + 1
= 2 x² + 2 x + x + 1
= 2 x² + 3 x + 1
