Finding the Limit of x^2-1/|x-1| at x=1

  • Thread starter Thread starter n.a.s.h
  • Start date Start date
  • Tags Tags
    Limit
n.a.s.h
Messages
18
Reaction score
0

Homework Statement



Finding a limit? x^2-1/| x-1|?

when x approaches 1 from the right

and when x approaches 1 from the left


Homework Equations





The Attempt at a Solution



for the right i got 2 and left i got -2 but I am not sure...
 
Physics news on Phys.org
That's right. I'd feel a little more confident that you understood it if you'd explain why.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
Replies
5
Views
2K
Limit and Integration of ##f_n (x)##
Replies
8
Views
2K
Calculate the limit cos(x)/sin(x) when x approaches 0
Replies
12
Views
3K
What Happens to f(x) as x Approaches 2?
Replies
15
Views
1K
Prove that ##\lim\limits_{x \to \infty} f(x) = 0##
Replies
3
Views
584
Solving differential equation (t^2-1)y''-6y=1
Replies
2
Views
822
Calculating radius of gyration of plane figure about x-axis
Replies
5
Views
2K
Volume between a region (above x-axis and below parabola) and a surface
Replies
4
Views
2K
Find limit of multi variable function
Replies
10
Views
1K
Use Graph to Determine Limit: Calculating Limits with Piecewise Functions
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top