Solving calculus problems in Higher Mathematics No one has answered all the time. I can only resend it

Solving calculus problems in Higher Mathematics No one has answered all the time. I can only resend it

Part by part integration method:
Original formula = 1 / 3 ∫ 0-1 f (x) d (x ^ 3)
=1 / 3 [f (x) x ^ 3] 0-1 - [1 / 3 ∫ 0-1 x ^ 3 D (f (x))] where d (f (x)) = SiNx / x ^ 2. (2x + 3)
=1/3(arc4-arc1) -[1/3∫0-1( 2x^2+3x)sinx dx ]
=1/3(arc4-arc1)-1/3(7sin1-cos1-4)

How to prove that the limit of SiNx divided by X is equal to 1

When x is replaced by - x in formula (1), formula (1) remains unchanged, so formula (1) holds when - π / 2 & lt; X & lt; 0, so that it holds for all x satisfying the inequality 0 & lt; X & lt; π / 2. From Lim (x → 0) cosx = 1 and the forced convergence of function limit, LIM (x → 0) SiNx / x = 1

The limit of F (x) divided by X is 1 when x tends to o, and the second derivative of F (x) is greater than 0. It is proved that f (x) is greater than or equal to x?
Proof by McLaughlin formula

What is the limit of Limin (1-1 / 2x ^ 2) * (3x ^ 2 + 1) when x tends to infinity and the detailed process

(1 + 2x) (1-3x) (1 + 4x) (1 + 6x) / (1 + 6x). When x tends to infinity, seek the limit! Which expert can you?
Root sign (1 + 3x ^ 2) - root sign (1-2x ^ 2) / 2x ^ 2, when x tends to 0, it takes a process to find the limit! Thank you
Is (1 + 2x) (1-3x) (1 + 4x) (1 + 6x) / (1 + 6x) ^ 4. X tends to infinity to find the limit

If the numerator and denominator are divided by (1 + 6x) x ^ 3, the limit is 2 * (- 3) * 4 / 6 ^ 3 = - 1 / 9
Lim radical (1 + 3x ^ 2) - radical (1-2x ^ 2) / 2x ^ 2
=Lim5x ^ 2 / {(2x ^ 2) [root (1 + 3x ^ 2) + root (1-2x ^ 2)]}
=LIM5 / {2 [radical (1 + 3x ^ 2) + radical (1-2x ^ 2)]}
=5/4.

Symmetry axis and vertex of square-2 of y = 1 / 3x

Y = 1 / 9x ^ 2-2 quadratic function symmetry axis = - B / 2A = 0 vertex when x = 0, y = - 2 (0, - 2)

Y = 3x square - 7x + 6 the coordinates of the vertex are

The axis of symmetry is x = 7 / 6
Substituting y = 3x 49 / 36 - 49 / 6 + 6 = 6 - 49 / 12 = 23 / 12
Coordinates are (7 / 6, 23 / 12)

It is known that the vertex of the parabola y = - half x ^ (2) + 3x - half is a, which is related to the X axis
It is known that the vertex of the parabola y = - half x ^ 2 + 3x - half is a, the two intersections with the X axis are B and C (B is on the left), the intersection with the Y axis and the point D, so as to find the area of the quadrilateral ABCD

Y = - x ^ 2 / 2 + 3x-5 / 2, the vertex coordinate is (- B / 2a, (4ac-b & # 178;) / 4A), i.e. a (3,2) - x ^ 2 / 2 + 3x-5 / 2 = 0, the solution is X1 = 1, X2 = 5, i.e. B (1,0) C (5,0) point d (0, - 5 / 2) s △ ABC = 0.5 * (5-1) * 2 = 4S △ BCD = 0.5 * (5-1) * I-5 / 2I = 5, the area of quadrilateral ABCD = 4 + 5 = 9 is unclear

Which simple functions are combined to form the function y = sin2 (E2x + 1)
RT

y=u²
u=sinv
v=s+1
s=t²
t=e^x

Limx approaches infinity (x ^ 3 + 5) / (2x ^ 2 + 3x-5)

Divide by x ^ 2
You can figure it out
lim (x+5/x^2)/(2+3/x-5/x^2)
=limx/2
=Infinity