Question

Use the Maclaurin series for cos(?) , ????(?), and ?^{?}
to evaluate the following limits:

a. lim ?→0 −? − 1+?^{x} / 5? 2 .

b. lim ?→0 ? − ???? / ?^{3} ????

Answer #1

Use a Maclaurin series in this table to obtain the Maclaurin
series for the given function.
f(x) = 8x cos(1/5x^2)

Find the Maclaurin series of f(x) = cos^2 (x)

Find the Maclaurin Series of f(x) = cos^2(x)

please show all work Evaluate each of the following limits, for
after lim the part with x-> and then a number is below the lim
and then after is the fraction part
1) lim x->3 (x^2-2x-3/x^2-5x+6)
2) limx->2 (x-2/square root(2x)-2)
3) lim x->inf (3x^5-7x^3/-5x^5+x^3-9)

1. Evaluate the limit
lim x→0 sin4x /7x
2. In which limits below can we use L'Hospital's Rule? select
all that apply.
lim x→∞ e^−x /x
lim x→0 1−e^x /sin(2x)
lim x→0 x+tanx /sinx
lim x→−∞ e^−x /x

find a maclaurin series using a derived formula of
f(x)=cos(x^2)

Evaluate each of the following limits. a) limx→∞(x/x − 2)^x
b) limx→0 sin x cos x/x + tan x

Use a Maclaurin series in this table to obtain the Maclaurin
series for the given function.
f(x) = e4x + 6e−4x

Finding Limits: Use L’Hopital’s rule to evaluate the limit .
SHOW WORK .
8. lim┬(x→-1)〖(x-8x^2)/(12x^2+5x)〗
9. lim┬(x→0)〖sin5x/(2x^2 )〗

Use L'Hopitals Rule to evaluate the following limit.
lim x-> 0 ( sin(8x) - 8x cos(8x) ) / ( 8x - sin(8x) )
Please use L'Hopitals Rule please

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