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erica [24]
3 years ago
6

Each limit represents the derivative of some function f at some number a. State such an f and a in each case.

Mathematics
1 answer:
vodka [1.7K]3 years ago
5 0

Answer:

<h2>a = 0</h2><h2>f(h) = \frac{\sqrt{9+h} - 3}{h}</h2><h2>limit of the function is 1/6</h2>

Step-by-step explanation:

The general form representing limit of a function is expressed as shown below;

\lim_{h \to a} f(h) where a is the value that h will take and use in the function f(h). It can be expressed in words as limit of function f as h tends to a. Comparing the genaral form of the limit to the limit given in question \lim_{h \to 0} \frac{\sqrt{9+h} - 3}{h}, it can be seen that a = 0 and f(h) = \frac{\sqrt{9+h} - 3}{h}

Taking the limit of the function

\lim_{h \to 0} \frac{\sqrt{9+h} -3}{h}\\= \frac{\sqrt{9+0}-3 }{0}\\= \frac{0}{0}(indeterminate)

Applying l'hopital rule

\lim_{h \to 0} \frac{\frac{d}{dh} (\sqrt{9+h} - 3)} {\frac{d}{dh} (h)}\\= \lim_{h \to 0}  \frac{1}{2}  (9+h)^{-1/2} /1\\=\frac{1}{2}  (9+0)^{-1/2}\\= \frac{1}{2}  * \frac{1}{\sqrt{9}  } \\= 1/2 * 1/3\\= 1/6

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Linear equations 3(x+1)=3x+3
vaieri [72.5K]
4x + 2 - 3x + 5 - 2(x + 5) = (2x - 5) + (3x + 4) 
4x + 2 - 3x + 5  - 2x - 10 =   2x - 5 +   3x + 4 
4x - 3x - 2x + 5 + 2 - 10  =  2x + 3x - 5 + 4 
        - x             - 3           =       5x       - 1   
-x - 3 = 5x - 1 is the line above recopied 
+x     = +x       
    -3   = 6x - 1 
<span>    +1   =    + 1 </span>
    - 2   = 6x 
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3 0
3 years ago
What are proofs statements
mina [271]

Geometric proofs can be written in one of two ways: two columns, or a paragraph. A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof, we'll learn the two-column method.

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5 0
3 years ago
Can someone help me please
Nat2105 [25]
Ithe diameter would be about 5
4 0
2 years ago
Read 2 more answers
The volume of a large aquarium is 210 yd. It is 3 yd wide and 2
Pavel [41]

Length of the aquarium is 35 yd

Step-by-step explanation:

  • Step 1: Volume of the aquarium = 210 yd³ given by Volume = length × width × height. Width = 3 yd and Height = 2 yd

Length = Volume/Width × Height

            = 210/3 × 2 = 210/6

            = 35 yd

5 0
3 years ago
The night watchman in a factory cannot guard both the safe in back and the cash register in front. The safe contains $6000, whil
Zolol [24]

Answer:

The guard should be positioned at the safe

Step-by-step explanation:

The night watchmen should be positioned to guard whichever place gives the highest expected value to the thief.

The expected value of robbing the safe is:

EV_{s} = \$ 6000*0.2\\EV_{s} = \$ 1200

The expected value of robbing the cash register is:

EV_{r} = \$ 1000*0.8\\EV_{r} = \$ 800

Therefore, the guard should be positioned at the safe since it yields a higher expected value to the thief in case he tries to rob it.

7 0
3 years ago
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