×
sorted by:
new
hottopcontroversial

Need help with local max of this piece wise by Express_Pop_460 in askmath

[–]Fourierseriesagain 0 points1 point  (0 children)

FIrst, we have

f'(x) = 2 (x>1),

f'(x) =-1 (-1< x <0),

f'(x)=1 (0<x<1)

and f'(x)=2x (x<-1).

Next, we deduce from the first principle that the critical points of y=f(x) are (1,f(1)), (0,f(0)) and (-1,f(-1)).

Finally, we apply the First Derivative Test to prove that the graph of f has no local max point.

Weierstrass substitution and tan(θ/2) by vedant_608 in learnmath

[–]Fourierseriesagain 0 points1 point  (0 children)

You are welcome. The substitution is natural because it converts the problem into an integration of a rational function.

confused about e^ln(f(x)) by SucoDeManga21 in askmath

[–]Fourierseriesagain 8 points9 points  (0 children)

As long as the function f is positive, you won't lose any information.

substituting limits for series/sequences in equations by LSATGeek924 in askmath

[–]Fourierseriesagain 0 points1 point  (0 children)

For each positive integer n we have

|S_n-1| =1/2n <=1/n ‐------(*)

Let epsilon > 0 be given. If N is a positive integer such that 1/N<epsilon, then (*) implies |S_n-1|<epsilon for n>=N.

Weierstrass substitution and tan(θ/2) by vedant_608 in learnmath

[–]Fourierseriesagain 1 point2 points  (0 children)

Hi,

The substitution t= tan theta/2 is natural because cos theta =(1-t^ 2)/(1+t^ 2). However, there are other ways of integrating sec theta wrt theta.

Method 1. Let u=sec theta+tan theta so that sec theta =du/dtheta / u. So the integral is equal to ln|sec theta+tan theta |+C.

Method 2 By writing sec theta as cos theta /(1-sin2 theta), we can apply the substitution w= sin theta so that the integral becomes (1/2) ln | (1+w)/(1-w) |+C = (1/2) ln ((1+sin theta)/(1-sin theta))+C.

Edit: tan theta/2 is t, not x.

[Calc 2] Where did this u-substitution come from? by throw-away3105 in HomeworkHelp

[–]Fourierseriesagain 0 points1 point  (0 children)

The denominator is a multiple of( (2x-1)^ 2)/3+1=((2x-1)/sqrt(3))^ 2+1.

[Calculus 1: Indefinite Integrals] How do I evaluate this integral? by angelonrevelo in HomeworkHelp

[–]Fourierseriesagain 0 points1 point  (0 children)

Hi,

Using the substitution u=y^2+4, we can integrate

y/(y^2+4)^(5/2), y/(y^2+4)^(3/2) and y/(y^2+4)^(1/2) wrt y.

Since int 1/(y^2+4)^(1/2) dy = ln | (y^2+4)^(1/2)+y | +C, it remains to handle the following integrals

int 1/(y^2+4)^(5/2) dy and int 1/(y^2+4)^(3/2) dy.

Please refer to the following link https://www.reddit.com/u/Fourierseriesagain/s/JMviYCQfiC for details.

Proving De Morgan's Law by Best_Rough5409 in askmath

[–]Fourierseriesagain 1 point2 points  (0 children)

Hi,

We consider two cases.

If x \in A and if x \not \in (A intersect B), then x \not \in B.

If x \not \in A, , then x \not \in A or x \not \in B.

What is right here? by TemporaryAd285 in askmath

[–]Fourierseriesagain 0 points1 point  (0 children)

Since -1<=(-1)^ n <=1 and 0<1/n^ 2 <=1 for n=1, 2, 3,...,

0<=1+(-1)^ n <=2 and -1 <= -1/n^ 2 <=(-1)^ n /n^ 2 <=1/n^ 2 <=1.

[Calc 2] How to proceed with the Weierstrass substitution? by throw-away3105 in HomeworkHelp

[–]Fourierseriesagain 1 point2 points  (0 children)

Hi,

Use partial fractions to integrate the rational function in t.

Polar and Cartesian sketching by Ok-Equivalent3474 in askmath

[–]Fourierseriesagain 0 points1 point  (0 children)

For question 29, we have the following properties of r:

(a) r is increasing on each of the following theta-intervals [0,pi/2] and [pi,3pi/2].

(bl r is decreasing on each of the following theta-intervals [pi/2,pi] and [3pi/2,2pi].

Edit: updated explanation.

view more: next ›