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Tanzania [10]
3 years ago
11

Use the denition of the derivative to find f 0 (3), where f (x) = 3x+5 / 2x−1

Mathematics
1 answer:
Crazy boy [7]3 years ago
8 0

Answer:

f'(3)= -\frac{13}{25}

Step-by-step explanation:

We are asked to find f'(3) of function f(x)=\frac{3x+5}{2x-1} using definition of derivatives.

Limit definition of derivatives:

f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Let us find f(3+h) and f(3).

f(3+h)=\frac{3(3+h)+5}{2(3+h)-1}

f(3+h)=\frac{9+3h+5}{6+2h-1}\\\\f(3+h)=\frac{3h+14}{2h+5}

f(3)=\frac{3(3)+5}{2(3)-1}

f(3)=\frac{9+5}{6-1}\\\\f(3)=\frac{14}{5}

Substituting these values in limit definition of derivatives, we will get:

f'(3)= \lim_{h \to 0} \frac{f(3+h)-f(3)}{h}

f'(3)= \lim_{h \to 0} \frac{\frac{3h+14}{2h+5}-\frac{14}{5}}{h}

Make a common denominator:

f'(3)= \lim_{h \to 0} \frac{\frac{(3h+14)*5}{(2h+5)*5}-\frac{14(2h+5)}{5(2h+5)}}{h}

f'(3)= \lim_{h \to 0} \frac{\frac{5(3h+14)-14(2h+5)}{5(2h+5)}}{h}

f'(3)= \lim_{h \to 0} \frac{5(3h+14)-14(2h+5)}{5h(2h+5)}

f'(3)= \lim_{h \to 0} \frac{15h+70-28h-70}{5h(2h+5)}

f'(3)= \lim_{h \to 0} \frac{-13h}{5h(2h+5)}

Cancel out h:

f'(3)= \lim_{h \to 0} \frac{-13}{5(2h+5)}

f'(3)= \frac{-13}{5(2(0)+5)}

f'(3)= \frac{-13}{5(5)}

f'(3)= -\frac{13}{25}

Therefore, f'(3)= -\frac{13}{25}.

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enot [183]

Answer:

You will pay $1,300 in interest.

The final price of the car is of $14,300

Step-by-step explanation:

Simple interest formula:

I=P\ast r\ast t

In which:

I is the interest

P is the principal(initial value of the investment, amount borrowed,...)

r is the interest rate, as a decimal

t is the time, in years.

In this question:

Borrow $13,000, so P = 13000

4 years, so t = 4

Interest rate of 2.5%, so r = 0.025

I=13000\ast0.025\ast4=1300

You will pay $1,300 in interest.

Final price of the car:

Principal plus interest.

T=P+I=13000+1300=14300

The final price of the car is of $14,300

4 0
11 months ago
If nine times a certain number is subtracted from 7 the result is 52. Find the number.
mezya [45]

Answer:

Let the number to find be x

7 - 9x = 52

-9x = 52-7

- 9x = -45

Divide by - 9

x = 5

The number is 5

Hope this helps.

6 0
3 years ago
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Jenn equally shares 40 jellybeans with some friends. Is the number that each friends gets greater than 40 or less than 40? Expla
blagie [28]
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6 0
2 years ago
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ivanzaharov [21]

Answer:

1800

Step-by-step explanation:

Since there is the tragon fly beat his wings 30 times a second ,there is 60 hundredths of a second in a second multiply 30 x 60 and you should get 1800.

  1. mulitiply 0x0 = 0

     2.  mulitiply 6x0=0

        3. multiply 3x0=0

          4. mulitiply 6x3 = 18

            5. have 1800

or you can just multiply 6x3 = 18 and add the two zeros

6 0
3 years ago
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!
AleksAgata [21]
Your answer would be b.2 

6 0
2 years ago
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