Question

. Find the coefficient of x 5 in the expansion of (x + 2)13 .

Answer #1

which is in the form

General term is

We need co-efficient, i.e.

Now

Hence co-efficient of is

Consider the expansion of (x+1)8, which terms in the
expansion have a coefficient of 56?
x^4 and x^5
x^4 and x^6
x^3 and x^4
x^3 and x^5
What is the sum of coefficients in (x + 1)8?
512
128
364
256

what is the coefficient of x^4Y^6 In the expansion of
(2x-y^2)^7

Find an expression for the coefficient of thermal expansion 1.
for an ideal gas 2. for van der waals
show all your work

Given the volume expansion coefficient of water is 2.10 x
10-4 °C-1 and the volume expansion
coefficient of ethanol is 11.0 x 10-4 °C-1,
explain why ethanol is a better choice for use in a thermometer
than water.

what is the coeffficient of x^6 in the expansion of (x+2)^10 +
x^3(x+2)^5

Find the power series expansion for f(x) = x^2 e^(x^2) centered
at a = 0 and centered at a=-3

Find the power series expansion for the function g ( x ) = 2 x
/( 1 + 4 x ^2 )^ 2. Your answer should describe the process you
used to arrive at this answer.

Find the Fourier sine expansion of
f(x) = x for 0 < x < 1
2- x for 1 < x <2 (at least the first 4 nonzero term)

. Let f(x, y) = x2 y(2 − x + y2
)5 − 4x2 (1 + x + y)7 +
x3 y2 (1 − 3x − y)8 . Find the
coefficient of x5y3 in the expansion of f(x,
y).

Known f (x) = sin (2x)
a. Find the Taylor series expansion around x = pi / 2, up to 5
terms only.
b. Determine Maclaurin's series expansion, up to 4 terms only

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