Binomial Expansion

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Question 73

A model for the energy output, $E (x)$ , of a specialized transducer under mechanical stress is defined by the function $E(x) = (3 + 4x)^4$ , where $x$ is the applied strain. The expansion of this function is given by

3 + 4x)^4 = A + Bx + 864x^2 + 768x^3 + 256x^4

a.

Find the values of the constants $A$ and $B$ .

[2]

b.

Show that

3 + 4x)^4 - (3 - 4x)^4 = Cx + Dx^3

where $C$ and $D$ are constants to be found.

[3]

c.

Hence, or otherwise, find

\int \left( (3 + 4x)^4 - (3 - 4x)^4 \right) dx

[2]

Binomial Expansion

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Question 73

A model for the energy output, $E (x)$ , of a specialized transducer under mechanical stress is defined by the function $E(x) = (3 + 4x)^4$ , where $x$ is the applied strain. The expansion of this function is given by

3 + 4x)^4 = A + Bx + 864x^2 + 768x^3 + 256x^4

a.

Find the values of the constants $A$ and $B$ .

[2]

b.

Show that

3 + 4x)^4 - (3 - 4x)^4 = Cx + Dx^3

where $C$ and $D$ are constants to be found.

[3]

c.

Hence, or otherwise, find

\int \left( (3 + 4x)^4 - (3 - 4x)^4 \right) dx

[2]

Binomial Expansion

Question 73

Binomial Expansion Questions

Binomial Expansion

Question 73

Binomial Expansion Questions