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May
2
answered How can I solve the improper integral $\int_{1}^\infty {dx \over {(x+1)(x+2)}}$
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
RHS limit is $\infty$. As for the integral, IBP p times (is p an integer?). Long story short, show that it diverges for any $a>0$.
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
What I think you should look at, is whether $x^p$ term changes anything (probably not). Look at $\lim_{x \to 0} e^{\frac{1}{x}}x^p$ for example.
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
For $any$ a, finite or not
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
My point is that $\lim_{t \to 0} \int_{t}^{a} e^{\frac{1}{x}} dx$ doesn't exist
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
That's if, as you say, the upper bound is finite
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
The only interval of interest is $[0,1]$ because $\int_{0}^{1} e^{\frac{1}{x}}dx$ diverges
May
1
comment Show that $\int_0^{a} e^{1/x}x^p dx $ diverges for all $p$
do you mean as $a \to \infty$?
May
1
revised Prove that if $\sum_1^\infty a_n$ converges provided $a_n>0$ for all $n$, then $\sum_1^\infty \sqrt{a_na_{n+1}}$ converges too
edited body
May
1
answered Prove that if $\sum_1^\infty a_n$ converges provided $a_n>0$ for all $n$, then $\sum_1^\infty \sqrt{a_na_{n+1}}$ converges too
May
1
comment Need assistance solving a limit question without applying l'hopital's rule
I'm not sure I follow. The fact that there's a problem at $x= -\frac{5}{2}$ has nothing to do with what happens when $x \to -\infty$, because the question is about the limit, not continuity
May
1
answered Need assistance solving a limit question without applying l'hopital's rule
May
1
comment Which mathematical topics should an applied math major know to be employable in industry?
did you try searching for jobs in your area on indeed.com? Job ads often list specific requirements from applicants, e.g. this one: hcp.com/data-scientist-1
Apr
30
comment Proof by induction
It's at least the 3rd time I've seen this question in the last couple of days
Apr
30
answered Proof verification for proving $\forall n \ge 2, 1 + \frac1{2^2} + \frac1{3^2} + \cdots + \frac1{n^2} < 2 − \frac1n$ by induction
Apr
30
answered Simple Induction Proof
Apr
29
answered Getting rid of $2^n$ when solving $a_n=8a_{n-1}-20a_{n-2}+16a_{n-3}+2^n$ by characteristic roots
Apr
29
comment Why does $\lim_{n \to \infty} x^{1+1/(2n-1)}=|x|$?
The nearest thing I can think of is that $x = e ^{\log x}$, which is a frequent trick of finding limits iff $x>0$
Apr
27
comment Convergence of $\sum_{n=1}^\infty (2n^{10}+4n^5+1)/(4n^{15}+4n^{12}+5)$
I don't think it's important that the constant is positive. What's important is that it's a $constant$, and hence either both sums diverge, or converge,
Apr
27
answered Why is $\lim_{x\to e^+} (\ln x)^{1/(x-e)} =e^{1/e}$