sketch a neat, piecewise function with the following
instruction: 1. as x approach infinity, the limit...
sketch a neat, piecewise function with the following
instruction: 1. as x approach infinity, the limit of the function
approaches an integer other than zero. 2. as x approaches a
positive integer, the limit of the function does not exist. 3. as x
approaches a negative integer, the limit of the function exists. 4.
Must include one horizontal asymtote and one vertical asymtote.
Consider the function f (x) = x/(2x+1)*2 .
(i) Find the domain of this function. (Start...
Consider the function f (x) = x/(2x+1)*2 .
(i) Find the domain of this function. (Start by figuring out any
forbidden values!)
(ii) Use (i) to write the equation of the vertical asymptote for
this function.
(iii) Find the limits as x goes to positive and negative
infinity,
(iv) Find the derivative of this function.
(v) Find the coordinates at point A(..,…), where the
x-coordinate is 1. Use exact fractions, never a decimal
estimate.
(vi) Find the equation of the...
The Taylor series for the function arcsin(x)arcsin(x) about
x=0x=0 is equal to
∑n=0∞(2n)!4n(n!)2(2n+1)x2n+1.∑n=0∞(2n)!4n(n!)2(2n+1)x2n+1.
For this question,...
The Taylor series for the function arcsin(x)arcsin(x) about
x=0x=0 is equal to
∑n=0∞(2n)!4n(n!)2(2n+1)x2n+1.∑n=0∞(2n)!4n(n!)2(2n+1)x2n+1.
For this question, recall that 0!=10!=1.
a) (6 points) What is the radius of convergence of this Taylor
series?
Write your final answer in a box.
b) (4 points) Let TT be a constant that is within the radius of
convergence you found. Write a series expansion for the following
integral, using the Taylor series that is given.
∫T0arcsin(x)dx∫0Tarcsin(x)dx
Write your final answer in a box.
c)...
(a) Show that the function f(x)=x^x is increasing on (e^(-1),
infinity)
(b) Let f(x) be as...
(a) Show that the function f(x)=x^x is increasing on (e^(-1),
infinity)
(b) Let f(x) be as in part (a). If g is the inverse function to
f, i.e. f and g satisfy the relation x=g(y) if y=f(x). Find the
limit lim(y-->infinity) {g(y)ln(ln(y))} / ln(y). (Hint :
L'Hopital's rule)
Write a function
called TaylorSin.m that takes as input an array x, and positive
integer N,...
Write a function
called TaylorSin.m that takes as input an array x, and positive
integer N, and returns the Nth Taylor polynomial approximation of
sin(x), centered at a = 0. The first line of your code should
read
function s =
TaylorSin(x,N)
HINT: in computing k!,
use kfact = k*(k-1)*kfact since you are counting by 2
Find a general term (as a function of the variable n) for the
sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}.
Find a...
Find a general term (as a function of the variable n) for the
sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}.
Find a general term (as a function of the variable n) for the
sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…}
an=
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
(If it diverges to infinity, state your answer as inf . If it
diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer...
Sigma n=1 to infinite (-1)^n sin(pi/n)
I confuse about this alternative test
I know this function...
Sigma n=1 to infinite (-1)^n sin(pi/n)
I confuse about this alternative test
I know this function F(x) = sin(pi/n) should be decreasing for
all n value.
but it is not decreasing when n =1 , n=2
but the answer is convergent.
so how I figure out this one, is it okay to ignore when n is 1
or 2? then why? cause the condition said, Function must be
decreasing for all n value.