Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: 

Derivative Property [Addition/Subtraction]: 

Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Reverse Power Rule]: 

Integration Property [Multiplied Constant]: 

Integration Methods: U-Substitution and U-Solve
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given.</em>
<em />
<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution/u-solve</em>.
- Set <em>u</em>:
  
- [<em>u</em>] Differentiate [Derivative Rules and Properties]:
  
- [<em>du</em>] Rewrite [U-Solve]:
  
<u>Step 3: Integrate Pt. 2</u>
- [Integral] Apply U-Solve:
  
- [Integrand] Simplify:
  
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
  
- [Integral] Apply Integration Rule [Reverse Power Rule]:
  
- [<em>u</em>] Back-substitute:
  
∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
 
        
             
        
        
        
In the bag there’s is 5 blue and only 2 green she is most likely gonna pick blue. Who would even want to know that
        
                    
             
        
        
        
5+4=9 es uno 4+5=9 es Otro 9-5=4 es Otro 9-4=5
        
             
        
        
        
it would be > because the square root of 2 is more than 1. 
 
        
                    
             
        
        
        
Answer:
Step-by-step explanation:
Given that,
f(3) = 2
f'(3) = 5.
We want to estimate f(2.85)
The linear approximation of "f" at "a" is one way of writing the equation of the tangent line at "a".
At x = a, y = f(a) and the slope of the tangent line is f'(a).
So, in point slope form, the tangent line has equation
y − f(a) = f'(a)(x − a)
The linearization solves for y by adding f(a) to both sides
 f(x) = f(a) + f'(a)(x − a).
Given that,
f(3) = 2, 
f'(3) = 5
a = 3, we want to find f(2.85) 
x = 2.85
Therefore,
f(x) = f(a) + f'(a)(x − a)
f(2.85) = 2 + 5(2.85 - 3)
f(2.85) = 2 + 5×-0.15
f(2.85) = 2 - 0.75
f(2.85) = 1.25