<munder> <mo form="prefix">lim <mrow class="MJX-TeXAtom-ORD"> x &#x2192;<!--

dglennuo 2022-05-28 Answered
lim x ( 4 5 + cos x ) prove that the limit is not finite while x using Cauchy definition
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

stacan6t
Answered 2022-05-29 Author has 13 answers
Suppose that limit L exists. For ϵ = 1 10 such that x > M 1 | f ( x ) L | < 1 10
Let N 1 N be such that 2 π N 1 > M 1 . Then if
n > N 1 2 n π > 2 π N 1 > M 1 | f ( 2 n π ) L | < 1 10 | 2 3 L | = | 4 5 + cos ( 2 n π ) L | < 1 10 Next for
ϵ = 1 15 , M 2 such that x > M 2 | f ( x ) L | < 1 15 . Again, let N 2 N be such that ( 2 N 2 + 1 ) π > M 2 . So if
n > N 2 ( 2 n + 1 ) π > ( 2 N 2 + 1 ) π > M 2 | f ( ( 2 n + 1 ) π ) L | < 1 15 | 1 L | < 1 15
Thus if n > N 1 + N 2 1 3 | 1 L | + | 2 3 L | < 1 10 + 1 15 = 1 6 1 3 < 1 6
Contradiction. So the limit Lcannot exists
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2020-12-16

The figure shows the surface created when the cylinder y2+Z2=1 intersects the cylinder x2+Z2=1. Find the area of this surface.
The figure is something like:
image

asked 2022-06-27
How to find the general antiderivative of f ( x ) = x ( 6 x ) 2 ?
I want to find the general antiderivative of f ( x ) = x ( 6 x ) 2 . However, I keep getting it wrong.
I am new to antiderivatives, but I think the first thing I should do is differentiate.
d d x ( 6 x ) 2 = 2 ( 6 x ) 1 = 2 ( 6 x )
f ( x ) = [ ( 6 x ) 2 1 ] + [ 2 ( 6 x ) x ] = ( 6 x ) 2 2 x ( 6 x )
According to the antiderivative power rule, when n 1, x n d x = x n + 1 n + 1 + C.
So it seems like ( 6 x ) 2 d x = ( 6 x ) 3 3 + C.
However, I can't find a rule that seems like it would work with 2 x ( 6 x ). The closest thing that I can find is the "Multiplication by Constant Rule", c f ( x ) d x = c ( f ( x ) ) d x, but I'm not sure if I'm allowed to change 2 x ( 6 x ) into the form 2 ( 6 x x 2 ).
2 ( 6 x x 2 )
= 2 ( 6 x x 2 )
= 2 ( 6 x x 2 )
= 2 ( 6 x 2 2 x 3 3 ) + C
But ( 6 x ) 3 3 ( 6 x 2 2 x 3 3 ) + C is incorrect.
asked 2021-12-30
What is the derivative of 5x ?
asked 2022-04-13
Is f(x)=x5+3x49x32x26x concave or convex at x=3?
asked 2021-10-07
Analyzing the Motion of a Projectile A projectile is fired
at an inclination of 45 to the horizontal, with a muzzle
velocity of 100 feet per second. The height h of the projectile
is modeled by h(x)=32x21002+x
where x is the horizontal distance of the projectile from the firing point
(a) At what horizontal distance from the firing point is the height of the projectile a maximum?
(b) Find the maximum height of the projectile.
(c) At what horizontal distance from the firing point will the projectile strike the ground?
(d) Using a graphing utility, graph the function h, 0x350 .
asked 2021-02-11
Find the limits. limx32(x21x)
asked 2022-06-01
Using the Cauchy integral formula show that
| z | = 2 e z d z ( z 1 ) 2 ( z 3 ) = 3 2 j e π .

New questions