Is the complex derivative speed November 28    3

The first thing I was told about the real derivative is that it's "how fast the function is growing" at a given point. This interpretation wasn't addressed in my complex analysis classes. Can the complex derivative also be interpreted as "s

Taking the derivative of $x^{\sin(e^x)}$ November 28    2

How am I suppose to take the derivative of $f(x)=x^{\sin(e^x)}$?What should I make $u$ equals?I tried to make $u=\sin(e^x)$ and $u=e^x$ but they didn't work.Hint: Here, you want to (start off) by using logarithmic differentiation - that is, take the

Palindrome Induction Proof November 28    1

Consider strings made up only of the characters $0$ and $1$; these are binary strings. A binary palindrome is a palindrome that is also a binary string.(a)Let $f(n)$ be the number of binary palindromes of length $2n$, for $n\ge 0$. Discover a formula

Prove by induction on strings November 28    1

I have this question: Prove by induction on strings that for any binary string w, (oc(w))^R = oc(w^R). note: if w is a string in {1,0}*, the one's complement of w, oc(w) is the unique string, of the same length as w, that has a zero wherever w has a

Prove reversal of a string by induction November 28    1

I am trying to prove that:(uv)R = vRuRwhere R is the reversal of a String defined recursively as:aR = a (wa)R = awRI think I have the base case right, but I am having trouble with the inductive step and final is what I have:Base Stepprove

Inductive Definition on the set of strings November 28    1

Given:$$ \Sigma = \{ a, b, c \}. $$I am trying to give the inductive definitions of both the set of strings $\Sigma^*$ and $\Sigma^+$.Thank you.The set $\Sigma^*$ contains all strings. The set $\Sigma^+$ contains all non-empty strings.Your inductive

Even-order derivative of $y = x\sin (x)$ November 28    1

How do I find the general formula for the even-order derivative of $y = x\sin (x)$?I tried using integration by parts and separation followed by mathematical induction, but I failed to obtain the correct answer, which is:$$\frac {\mathsf d^{2n}y}{\ma

n-th derrivative of f(lnx) November 28

Find general formula for $n$-th derrivative of $y = f(lnx)$.To start with I found couple of derrivatives:$y'={1 \over x}f'(lnx)$$y''={1 \over x^2}(f''(lnx)-f'(lnx))$$y'''={1 \over x^3}(f'''(lnx)-f''(lnx))$$y''''={1 \over x^4}(f''''(lnx)-6f'''(lnx)+11

Q: Two independent sequences of Bernoulli trials November 28

I'm trying to solve the following problem:Two players conduct simultaneously and independently a sequence of Bernoulli trials. Both have a probability $p$ for success in each Bernoulli trail. What is the probability that the first player will have $i

lim sup and lim infs of Brownian Motion November 28

lim sup and lim infs of Brownian Motion
Below is my question. Q7.9 is what I'm stuck on. I've done Q7.8; I included it in the picture because I'll use it in Q7.9, and it gives a definition that I'll use.What I've done so far is th ...

Piecewise monotonicity of real analytic functions November 28

This may have a completely trivial answer, but I don't see it at the moment:If the series expansion $f(x)=\sum_n a_n x^n$ is valid on the whole of $\mathbb{R}$, must there exist a countably infinite partition $$\ldots r_{-2} < r_{-1} < r_0 < r_1

Coordinate Geometry:Locus Based Problem November 28    1

A rod AB of length l slides with its ends on the coordinate axes.Let O be the origin.The rectangle OAPB is completed. How to prove the locus of the foot of perpendicular drawn from P onto AB is $x^{2/3}+y^{2/3}=l^{2/3} $ ?Let $N(x,y)$ be the foot of

You Might Also Like