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hammer [34]
4 years ago
6

Find the sum of the coefficients in the expansion of (x+1)^12

Mathematics
1 answer:
MariettaO [177]4 years ago
4 0

Answer:

<h2>2¹²</h2>

Step-by-step explanation:

The sum of the coefficients in the expansion of (x+1)^12:

= 12C0 + 12C1 + 12C2 + . . . + 12C11 + 12C12

the formula says that this sum equal to 2¹².

Other examples

The sum of the coefficients in the expansion of (x+1)^3:

3C0+3C1+3C2+3C3

=8 = 2³

The sum of the coefficients in the expansion of (x+1)^4:

4C0+4C1+4C2+4C3+4C4

=16 = 2⁴

:)

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Answer:

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Step-by-step explanation:

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3 years ago
Which is the graph of f (x) = 4 (1/2) Superscript x?
miss Akunina [59]

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

f(x)=4(\frac{1}{2})^x

Now, the above function is an exponential function of the form f(x)=ka^x

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

f(0)=4(\frac{1}{2})^0=4

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0

So, as

x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty

Now, from among all the options, only option (2) fulfills all the conditions given above.

So, option (2) is correct graph.

5 0
4 years ago
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Answer:

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Step-by-step explanation:

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3) Factor out the common term 3x+4.

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