Recent content by JustinDaniels

I observed the range of values to be ##-1 < x < 5##. Thus, the radius of convergence is 3. The next question in this assignment asks us to find a property of the function that explains why the radius is what it is. I see no relationship between the two however.

Okay, spoke to my professor. The limit of the ratio test evaluates out to ##\frac{1}{3} |x-2|##, which I essentially had in the previous post. We note that this value is not dependent on ##k##, so that when k goes to infinity the limit stays as ##\frac{1}{3} |x-2|##. The range of x values that...

Okay, so I incorrectly defined ##a_n## and ##a_{n+1}##; as a result, I misapplied the Ratio Test. ##a_{n+1}## should be ##\frac{1}{9} \frac{1}{k+1} (4-3k) c_{k} (x-2)^{k+1}## In reapplying the Ratio Test, I observe the following: ##lim_{k \rightarrow \infty} |\frac {\frac{1}{9} \frac{1}{k+1}...

I'm quite confused.. Here is what I get for the first six terms in the Taylor series: Term 0: ##(1+(2))^{4/3}## Term 1: ##4/3 (1+2)^{1/3}(x-2)## Term 2: ##\frac{(4/9) (1+2)^{-2/3}}{2!} (x-2)^2## Term 3: ##\frac{-(8/27) (1+2)^{-5/3}}{3!} (x-2)^3## Term 4: ##\frac{(40/81) (1+2)^{-8/3}}{4!}...

So I need an additional factor of (1/3)? I have the formula containing a 3-1, which is 1/3. Also, ##c_k## is the coefficient of the kth term in the series (i.e. the number before the ##x-2##), therefore I do not think it needs a factor of ##x-2##. Note, the coefficients of the series are: f(x)...

Homework Statement Let f(x)= (1+x)4/3 - In this question we are studying the Taylor series for f(x) about x=2. This assignment begins by having us find the first 6 terms in this Taylor series. For time, I will omit them; however, let's note that as we continuously take the derivative of this...

Edit: I forgot to take the cubic root of the radius when solving in step 3. Sorry for the pointless thread, and thank you guys anyway!

Homework Statement What is the diameter of a copper sphere that has the same mass as a 9.00 cm× 9.00 cm× 9.00 cm cube of aluminum? Density of Aluminum = P(al) = 2.70g/cm3 Density of Copper = P(cu) = 8.96 g/cm3 Volume of Aluminum Cube = Vcube = 729 cm3 Homework Equations Volume of a Sphere =...