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5 działań(-nia) podobnych(-ne) do:

x \to 0 lim 5 x

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Prove that for any

c \neq = 0

lim_{x \to c} h (x)

does not exist and that

lim_{x \to 0} h (x)

https://math.stackexchange.com/questions/334631/prove-that-for-any-c-neq-0-lim-x-rightarrow-chx-does-not-exist-and

Hint: take one sequence that contains only rationals and another one that contains only irrationals (both tending to

c \neq = 0

). For the case of

c = 0

, you can use e.g. that

h

is continuous at

0

Proofs regarding Continuous functions 1

https://math.stackexchange.com/questions/526691/proofs-regarding-continuous-functions-1

The proof of part a) needs to be modified a bit. You have used the logic that if

N \leq f (x) \leq M

x N \leq x f (x) \leq x M

. This holds only when

x \geq 0

. It is better to change the argument ...

Use L'Hopital's with this problem?

https://math.stackexchange.com/questions/1419122/use-lhopitals-with-this-problem

y = x \to 0^{+} lim (\frac{1}{x})^{s i n x},

x = 0 + h,

y = h \to 0 lim (\frac{1}{h})^{s i n h}

ln (y) = h \to 0 lim sin (h) \cdot ln (\frac{1}{h}) = - h \to 0 lim sin h \cdot ln (h) = - h \to 0 lim \frac{ln ( h )}{csc ( h )} (\frac{\infty}{\infty})

lim_{x \to 0} = x \cdot sin (\frac{1}{x})

https://math.stackexchange.com/questions/1066434/calculate-lim-x-to-0-x-cdot-sin-frac1x

Your proof is incorrect, cause you used incorrect transform, but it has already been stated. I'll describe way to solve it.

lim_{x \to 0} \frac{s i n ( \frac{1}{x} )}{\frac{1}{x}} \neq = 1

f (x)

is bounded. Please check my proof.

https://math.stackexchange.com/q/1052420

Here is another approach: Let

L_{0} = lim_{x ↓ 0} f (x), L_{\infty} = lim_{x \to \infty} f (x)

. By definition of the limit we have some

δ > 0

N > 0

x \in (0, δ)

Complex Function limit by investigating sequences

https://math.stackexchange.com/questions/1915934/complex-function-limit-by-investigating-sequences

z \to 0

exists, one should be able to plug in any sequence

{z_{n}}

going to zero and get the same limit. Limits of sequences are generally easier to work with. So in this case if ...

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Przykłady

Równanie kwadratowe

x^{2} - 4 x - 5 = 0

4 sin θ cos θ = 2 sin θ

Równanie liniowe

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

Równania równoważne

{8 x + 2 y = 46 7 x + 3 y = 47

Różniczkowanie

\frac{d}{d x} \frac{( 3 x ^{2} - 2 )}{( x - 5 )}

\int_{0}^{1} x e^{- x^{2}} d x

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}