Microsoft Math Solver
Oplossen
Oefenen
Download
Solve
Practice
Onderwerpen
Pre-Algebra
Gemiddelde
Modus
Grootste Gemene Deler
Kleinste Gemene Veelvoud
Bewerkingsvolgorde
Breuken
Gemengde Breuken
Ontbinding in priemfactoren
Exponenten
Wortels
Algebra
Combineer Soortgelijke Termen
Een variabele oplossen
Factor
Uitbreiden
Breuken evalueren
Lineaire Vergelijkingen
Vierkantsvergelijkingen
Ongelijkheden
Stelsels van vergelijking
Matrices
Trigonometrie
Vereenvoudigen
Evalueren
Grafieken
Vergelijkingen oplossen
Analyse
Afgeleiden
Integralen
Limieten
Algebracalculator
Trigonometrische calculator
Calculuscalculator
Grafische Rekenmachine
Download
Onderwerpen
Pre-Algebra
Gemiddelde
Modus
Grootste Gemene Deler
Kleinste Gemene Veelvoud
Bewerkingsvolgorde
Breuken
Gemengde Breuken
Ontbinding in priemfactoren
Exponenten
Wortels
Algebra
Combineer Soortgelijke Termen
Een variabele oplossen
Factor
Uitbreiden
Breuken evalueren
Lineaire Vergelijkingen
Vierkantsvergelijkingen
Ongelijkheden
Stelsels van vergelijking
Matrices
Trigonometrie
Vereenvoudigen
Evalueren
Grafieken
Vergelijkingen oplossen
Analyse
Afgeleiden
Integralen
Limieten
Algebracalculator
Trigonometrische calculator
Calculuscalculator
Grafische Rekenmachine
Oplossen
algebra
Trigonometrie
statistieken
analyse
matrices
variabelen
lijst
Evalueren
\frac{3}{2}=1.5
2
3
=
1
.
5
Quiz
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
x
→
−
3
lim
x
2
+
2
x
−
3
x
2
−
9
Vergelijkbare problemen van Web Search
What is the value of \displaystyle\lim_{{{x}\rightarrow-{3}}}{\frac{{{x}^{{{2}}}-{9}}}{{{x}^{{{2}}}-{2}{x}-{15}}}} ?
What is the value of
x
→
−
3
lim
x
2
−
2
x
−
1
5
x
2
−
9
?
https://socratic.org/questions/what-is-the-value-of-lim-x-rightarrow-3-frac-x-2-9-x-2-2x-15
\displaystyle\frac{{3}}{{4}} Explanation: \displaystyle\lim_{{{x}\to-{3}}}\frac{{{x}^{{2}}-{9}}}{{{x}^{{2}}-{2}{x}-{15}}} By factoring out the numerator and the denominator, \displaystyle=\lim_{{{x}\to-{3}}}\frac{{\cancel{{{\left({x}+{3}\right)}}}{\left({x}-{3}\right)}}}{{\cancel{{{\left({x}+{3}\right)}}}{\left({x}-{5}\right)}}}=\frac{{-{3}-{3}}}{{-{3}-{5}}}=\frac{{-{6}}}{{-{8}}}=\frac{{3}}{{4}} ...
4
3
Explanation:
x
→
−
3
lim
x
2
−
2
x
−
1
5
x
2
−
9
By factoring out the numerator and the denominator,
=
x
→
−
3
lim
(
x
+
3
)
(
x
−
5
)
(
x
+
3
)
(
x
−
3
)
=
−
3
−
5
−
3
−
3
=
−
8
−
6
=
4
3
...
Evaluating \lim\limits_{x\to-3}\frac{x^2-9}{2x^2+7x+3}
Evaluating
x
→
−
3
lim
2
x
2
+
7
x
+
3
x
2
−
9
https://math.stackexchange.com/q/490053
\require{cancel} Note that both the numerator and denominator evaluate to 0 at x = -3. That means we have an indeterminate limit, which simply means more work needs to be done. Factor ...
Note that both the numerator and denominator evaluate to
0
at
x
=
−
3
. That means we have an indeterminate limit, which simply means more work needs to be done. Factor ...
Help with epsilon-delta proof of \lim_{x \to -3} \frac{x^2 + x - 6}{x^2 - 9}
Help with epsilon-delta proof of
lim
x
→
−
3
x
2
−
9
x
2
+
x
−
6
https://math.stackexchange.com/questions/197844/help-with-epsilon-delta-proof-of-lim-x-to-3-fracx2-x-6x2-9
HINT: \frac{x^2+x-6}{x^2-9}-\frac56=\frac{6x^2+6x-36-(5x^2-45)}{6(x^2-9)}=\frac{x^2+6x+9}{6(x^2-9)}=\frac{(x+3)^2}{6(x-3)(x+3)}
HINT:
x
2
−
9
x
2
+
x
−
6
−
6
5
=
6
(
x
2
−
9
)
6
x
2
+
6
x
−
3
6
−
(
5
x
2
−
4
5
)
=
6
(
x
2
−
9
)
x
2
+
6
x
+
9
=
6
(
x
−
3
)
(
x
+
3
)
(
x
+
3
)
2
What is \displaystyle \lim_{x \to 1} \dfrac{x^2-1}{x^2+3x-4} ?
What is
x
→
1
lim
x
2
+
3
x
−
4
x
2
−
1
?
https://www.quora.com/What-is-displaystyle-lim_-x-to-1-dfrac-x-2-1-x-2+3x-4
You can see if you solve for x=1 that you get a fraction in the form of \dfrac{0}{0} which is indeterminate. When you get into a situation like this you can apply L'Hôpital's rule - Wikipedia. ...
You can see if you solve for
x
=
1
that you get a fraction in the form of
0
0
which is indeterminate. When you get into a situation like this you can apply L'Hôpital's rule - Wikipedia. ...
Proving that \lim_{x\to 2}\frac{x^2-5x}{x^2+2}=-1 using the \epsilon-\delta definition of a limit
Proving that
lim
x
→
2
x
2
+
2
x
2
−
5
x
=
−
1
using the
ϵ
-
δ
definition of a limit
https://math.stackexchange.com/questions/1872290/proving-that-lim-x-to-2-fracx2-5xx22-1-using-the-epsilon-delta
Let \epsilon>0 be given. We have to find a number \delta>0 such that \left|\frac{x^2-5x}{x^2+2}+1\right|<\epsilon whenever |x-2|<\delta. But, as Andre notes, \left|\frac{x^2-5x}{x^2+2}+1\right|=\left|\frac{2x^2-5x+2}{x^2+2}\right|=|x-2|\left|\frac{2x-1}{x^2+1}\right|. ...
Let
ϵ
>
0
be given. We have to find a number
δ
>
0
such that
∣
∣
∣
∣
x
2
+
2
x
2
−
5
x
+
1
∣
∣
∣
∣
<
ϵ
whenever
∣
x
−
2
∣
<
δ
. But, as Andre notes,
∣
∣
∣
∣
x
2
+
2
x
2
−
5
x
+
1
∣
∣
∣
∣
=
∣
∣
∣
∣
x
2
+
2
2
x
2
−
5
x
+
2
∣
∣
∣
∣
=
∣
x
−
2
∣
∣
∣
∣
x
2
+
1
2
x
−
1
∣
∣
∣
.
...
Limit simplification
Limit simplification
https://math.stackexchange.com/q/2704118
Note that \lim_{x\to -3} \frac{(x^2-9)^2}{x^2+\color{red}6x+9} We can solve in this way \lim_{x\to -3} \frac{(x^2-9)^2}{(x+3)^2}=\lim_{x\to -3} \frac{(x-3)^2(x+3)^2}{(x+3)^2}=\lim_{x\to -3} (x-3)^2=36
Note that
lim
x
→
−
3
x
2
+
6
x
+
9
(
x
2
−
9
)
2
We can solve in this way
lim
x
→
−
3
(
x
+
3
)
2
(
x
2
−
9
)
2
=
lim
x
→
−
3
(
x
+
3
)
2
(
x
−
3
)
2
(
x
+
3
)
2
=
lim
x
→
−
3
(
x
−
3
)
2
=
3
6
Meer Items
Delen
Kopiëren
Gekopieerd naar klembord
Voorbeelden
Vierkantsvergelijking
{ x } ^ { 2 } - 4 x - 5 = 0
x
2
−
4
x
−
5
=
0
Trigonometrie
4 \sin \theta \cos \theta = 2 \sin \theta
4
sin
θ
cos
θ
=
2
sin
θ
Lineaire vergelijking
y = 3x + 4
y
=
3
x
+
4
Rekenen
699 * 533
6
9
9
∗
5
3
3
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
[
2
5
3
4
]
[
2
−
1
0
1
3
5
]
Stelselvergelijking
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
{
8
x
+
2
y
=
4
6
7
x
+
3
y
=
4
7
Differentiëren
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
d
x
d
(
x
−
5
)
(
3
x
2
−
2
)
Integreren
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
∫
0
1
x
e
−
x
2
d
x
Limieten
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
x
→
−
3
lim
x
2
+
2
x
−
3
x
2
−
9
Terug naar boven