Given that f (x) is an even function, G (x) is an odd function, f (x) + G (x) = x ^ 2 + 2 ^ x, find f (1)

f(1)+g(1)=3
f(-1)+g(-1)=3/2
Because f (x) is even and G (x) is odd
So f (- 1) = f (1), G (- 1) = - G (1)
The above two formulas are f (1) + G (1) = 3, f (1) - G (1) = 3 / 2
If the two formulas are added, f (1) = 9 / 4 is obtained

F (T) is a continuous function. If f (T) is an odd function, it is proved that ∫ (0 → x) f (T) DT is an even function; if f (T) is an even function, it is proved that ∫ (0 → x) f (T) DT is an odd function

Let f (x) = ∫ (0 → x) f (T) DTF (- x) = ∫ (0 → x) f (T) DT = ∫ (0 → x) f (- t) d (- t) = - ∫ (0 → x) f (- t) DTF (T) be odd function, f (T) = - f (- t) f (- x) = ∫ (0 → x) f (T) DT = f (x) even function, f (T) = f (- t) f (- x) = - ∫ (0 → x) f (T) DT = - F

Finding the derivative of parametric equation x = f '(T), y = TF' (T) - f (T)
x=f'(t)
Y = TF '(T) - f (T)
[f'(t)+tf''(t)-f'(t)]/f''(t)...
What is the derivative of y = TF '(T) - f (T)
But why is the answer f '(T) + TF' '(T) - f' (T)

Y = TF '(T) - f (T) first of all, when this formula is derived from t, you need to make it clear, then y' is the derivative of TF '(T) and - f (T), TF' (T) is the derivative equivalent to (UV), where u is t, V is f '(T) (UV)' = u ` V + UV ', so [TF' (T)] '= t' * f '(T) + T * [f (T)]' = t '* f' (T) + T * [f (T)] '= t' * f '(T)' (T)] '= t' * f '(T) + T * [f (T)]' = t '* f' (T) '(T)' (T)

Help convert inch units into millimeters
I know that an inch is 25.4 mm. What does 13 "3 / 8 mean? How many mm is it?

13 and 3 / 8 inches, or 107 / 8 inches,
107 / 8 * 25.4 = 339.725mm

3. Given that the center line on the hypotenuse of the right triangle is 1, the perimeter is 2 + root 6, calculate the area of the triangle

The center line of the hypotenuse of a right triangle is half of the hypotenuse
So the hypotenuse is 2
Let the lengths of two right angle sides be a and B respectively
So a + B = root 6
And a + B = 2 ^ 2 = 4
The solution is a = (radical 6 + radical 2) / 2
B = (radical 6-radical 2) / 2
So the area s = a * B / 2 = 1 / 2
That is, the area of the triangle is 1 / 2

If the line y = ax + B (AB ≠ 0) is not the third quadrant, then the quadrant of the vertex of the parabola y = AX2 + BX is ()
A. One B. two C. three D. four

∵ if the line y = ax + B (AB ≠ 0) is in the third quadrant, then a ＜ 0, B ＞ 0, − B2A ＞ 0, 4ac − b24a ＞ 0, and the quadrant where the vertex of the parabola y = AX2 + BX is in is the first quadrant

How much does a cubic meter of water weigh

The maximum density of water is 1g / cm ^ 3 at 4 ℃. At this time, the mass of a cubic meter of water is 1000kg and the weight is 9800n (the acceleration of gravity g is generally 9.8N / kg)

Polynomials multiplied by polynomials are represented by letters

(a+b)(c+d)=ac+ad+bc+bd.
(a+b)(c+d+e)=ac+ad+ae+bc+bd+be.

Two random variables XY are not independent, and their covariance cov (x, y) is known. How to calculate the expected e (XY) of the product of the two?
Two random variables XY are not independent. Their expectation, variance and covariance cov (x, y) are known. How to calculate the expectation e (XY) of their product?
If we don't know the covariance and only know the continuous probability density functions f (x) and G (y) of X and y, is there any way to find e (XY)?

Using the covariance formula
COV(X,Y)=E[(X-E(X))(Y-E(Y))]=EXY-EX*EY
Then exy = cov (x, y) + ex * ey
If ex, ey and cov (x, y) are known, they can be calculated

Conversion table of mass units
Five quality conversion questions

1kg=( )g
1g=( )mg
1kg=( )mg
1 ton = () kg
3.6 tons = () mg
Answer: 1000
one thousand
one million
one thousand
three billion and six hundred million

Given that f (x) is an even function, G (x) is an odd function, f (x) + G (x) = x ^ 2 + 2 ^ x, find f (1)