Three mathematical problems of senior two! The concept of derivative and its geometric significance! Urgent! 1. Y = x ^ 2 + 1, find the slope of the tangent line at point P (1,2) and the equation of the tangent line 2. Given f (x) = x ^ 2, G (x) = x ^ 3, find the value of X suitable for f '(x) + 2 = g' (x) 3. The equation of motion of an object is s (T) = t + 2 / T. The average velocity of the object from t0 to t0 + △ T and the instantaneous velocity at t = t0 are obtained

Three mathematical problems of senior two! The concept of derivative and its geometric significance! Urgent! 1. Y = x ^ 2 + 1, find the slope of the tangent line at point P (1,2) and the equation of the tangent line 2. Given f (x) = x ^ 2, G (x) = x ^ 3, find the value of X suitable for f '(x) + 2 = g' (x) 3. The equation of motion of an object is s (T) = t + 2 / T. The average velocity of the object from t0 to t0 + △ T and the instantaneous velocity at t = t0 are obtained

The equation of the tangent is y = 2x2. F '(x) = 2x G' (x) = 3x ^ 2 to get 2x + 2 = 3x ^ 2, from which X3 can be obtained. Average velocity = [S (t0 + △ T) - S (T0)] / △ t = (△ T + 2 / △ T) / △ t = 1 + 2 / △ T ^ 2 instantaneous velocity = [S (T0)] '= (t0 + 2 / t0)' = 1-2 / t0 ^ 2

Given the set a = {y | y = log (base 2) logarithm of X, x > 1}, B = {y | y = (1 / 2) ^ x}, then a ∩ B =?

∵y=log2 x x>1
And ∵ 2 ∵ 1
∴y＞0
y=(1/2)^x
∵x∈R
∴y＞0
∴A∩B=｛y|y＞0}

As shown in the figure, it is known that △ ABC, P is a point on edge ab. when connecting CP, (1) ∠ ACP satisfies what conditions, △ ACP is similar to △ ABC?
When 2 AC; AP satisfies what conditions, △ ACP is similar to △ ABC

1. When ∠ ACP = ∠ B, △ ACP ∽ ABC,
2. When AC / AP = AB / AC, or written as AC & # 178; = AP * AB, or AP = AC & # 178 / / AB (three are equivalent, any one can be written)
△ACP∽△ABC.
If you still have doubts, please ask

Who can help me change these words into plural?
chinese japanese child man woman sheep tomato potato

chinese, japanese, children,men,women,sheep,tomatos,potatos

Circle C1: X & # 178; + Y & # 178; - 2x-6y-1 = 0, circle C2: X & # 178; + Y & # 178; - 10x-12y + M = 0?

Simplification (x-1) &# 178; + (Y-3) &# 178; = 11, (X-5) &# 178; + (y-6) &# 178; = 61-m
C1(1,3)C2(5,6)
C1C2=5
∵ circle C1 and circle C2 circumscribed
r1=√11,r2=√（61-m）
C1C2=r1+r2=5
m=25+10√11

Finding indefinite integral ∫ DX / √ 5-2x-x ^ 2
The process should be detailed

Let 1 + x = √ 6sinu, then: u = arcsin [(1 + x) / √ 6], DX = √ 6cosudu
∴∫［1/√（5－2x－x^2）］dx
＝∫｛1/√［6－（1＋x）^2］｝dx
＝√6∫｛1/√［6－6（sinu）^2］｝cosudu
＝∫（1/cosu）cosudu
＝u＋C
＝arcsin［（1＋x）/√6］＋C.

English translation
The second chapter introduces the background and significance of the study of reading. The third chapter analyzes the importance of reading in learning. The fourth chapter uses the mouth, ear and mouth reading teaching method to organize some reading classes, The fifth chapter analyzes some methods and habits of students in reading through some data. The sixth chapter summarizes the advantages of mouth, ear and mouth reading in teaching and reading

The second chapter introduces the background and significance of the study of reading. The third chapter analyzes the importance of reading in learning. The fourth chapter uses the mouth, ear and mouth reading teaching method to organize some reading classes, The fifth chapter analyzes some methods and habits of students in reading through some data. The sixth chapter summarizes the advantages of mouth, ear and mouth reading in teaching and reading
Translation:
The second chapter introduces the research background and the significance of reading. The third chapter analyses the importance of reading in learning; the fourth chapter teachers use mouthmouth reading teaching method combining with the reality of the students, to organize some reading, and through these courses for the students to improve their interest in learning. The fifth chapterthrough some data analysis methods of students in reading timeand some habits. The sixth chapter summarizes the mouth mouthreading in teaching and reading the advantage.

A shop bought a batch of badminton rackets. The purchase price was 30 yuan for each pair and the retail price was 40 yuan for each pair. When there were 100 pairs left, it recovered the money used to buy these rackets and made a profit of 100 yuan______ Yes

Suppose there are x pairs of these badminton rackets, (X-100) × 40-30x = 100, & nbsp; & nbsp; & nbsp; & 40x-4000-30x = 100, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 10x-4000 = 100, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 410; answer: there are 410 pairs of these badminton rackets

The area formula of parallelogram is expressed in letters______ ．

The area formula of parallelogram is expressed in letters: S = ah. So the answer is: S = ah

Find the function y = (Tan & sup2; x-tanx + 1) \ (Tan & sup2; X + TaNx + 1)

Let a = TaNx
Then a belongs to R
y=f(x)=(a²-a+1)/(a²+a+1)
ya²+ya+y=a²-a+1
(y-1)a²+(y+1)a+(y-1)=0
If a is a real number, the equation has a solution
So the discriminant is greater than or equal to 0
(y+1)²-4(y-1)²>=0
(y+1+2y-2)(y+1-2y+2)>=0
(3y-1)(y-3)