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geniusboy [140]
3 years ago
14

Find the linearization L(x) of the function at a. f(x) = x^4 + 2x^2, a = 1

Mathematics
1 answer:
gregori [183]3 years ago
8 0

The equation of the tangent line at x=1 can be written in point-slope form as

... L(x) = f'(1)(x -1) +f(1)

The derivative is ...

... f'(x) = 4x^3 +4x

so the slope of the tangent line is f'(1) = 4+4 = 8.

The value of the function at x=1 is

... f(1) = 1^4 +2·1^2 = 3

So, your linearization is ...

... L(x) = 8(x -1) +3

or

... L(x) = 8x -5

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Which expression is equivalent to log3(x + 4)?
dangina [55]

Answer:

log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.

Step-by-step explanation:

By the logarithm product rule, for two nonzero numbers a and b,

\log{(a \cdot b)} = \log{(a)} + \log{(b)}.

Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.

For example, 3(x + 4) is the number in the logarithm \log{[3(x + 4)]}. Since 3(x + 4) is a product of the two numbers 3 and (x + 4), the logarithm \log{[3(x + 4)]} can be split into two. By the logarithm product rule,

\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}.

However, \log{(x + 4)} cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.

5 0
3 years ago
Read 2 more answers
Mila and Ben use red and orange beads to make bracelets with 60 beads each.
aleksandr82 [10.1K]

Answer:

Mila

Step-by-step explanation:

3+2=5

60/5=12

12*3=36

Mila uses 36 orange beads

7+5=12

60/12=5

7*5=35

Ben uses 35 orange beads

Mila uses more beads

hope this helps you on your homework :D

5 0
2 years ago
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Shel bought a $6,000 desk based on her income she can only afford to pay 600 per month The charge on the unpaid balance is 2% ea
Irina18 [472]

Answer:

$5,030.40

Step-by-step explanation:

The balance outstanding at the end of any month is the due amount after adjusting for interest and loan repayment amount. The amount outstanding can be calculated as:

<u>First month</u>

Due amount = $6,000

Interest at 2% = $6,000*2% = $120

Loan repayment = $600

Reduction in balance = $600 - $120 = $480

Balance remaining = $6,000 - $480 = $5,520

<u>Second month</u>

Due amount = $5,520

Interest at 2% = $5,520*2% = $110.4

Loan repayment = $600

Reduction in balance = $600 - $110.4 = $489.60

Balance remaining = $5,520 - $489.60 = $5030.40

Hence, the balance outstanding at the end of month 2 is $5,030.40

3 0
2 years ago
What is the measure of the angle of elevation from point
IRINA_888 [86]

Answer:

53

Step-by-step explanation:

it's 53. i think they are called alternate angles

5 0
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