Pregunta
-
.
-
.
Ask by Romero Weaver. in China
Mar 17,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The limits are:
- 21.
- 27.
- 25.
- 24.
- 26.
Solución
21. Compute
Since the highest power in the numerator and denominator is
, we divide each term by
:
Taking the limit as
(so that
and
all go to 0):
27. Compute
First, expand the denominator:
Now, divide the numerator and denominator by
:
Taking the limit as
(observing that
and
):
25. Compute
As
, the denominator
increases without bound, so:
24. Compute
Divide numerator and denominator by
:
As
, both
and
approach 0, giving:
26. Compute
Expand the numerator:
The leading term in the numerator is
and the leading term in the denominator is
. Dividing numerator and denominator by
:
As
, all terms with
in the denominator approach 0:
Thus, the limits are:
- 21.
- 27.
- 25.
- 24.
- 26.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


The Deep Dive
When you’re tackling limits involving polynomials or rational functions, it’s often helpful to focus on the highest degree terms. For the first limit, both the numerator and the denominator are quadratic, so we only need to consider their leading coefficients. Simplifying gives you
.
In the limit
, expanding the denominator leads to
. Focusing again on the leading term gives
. Remember, in these types of limits, the highest degree terms dominate as
approaches infinity!

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium