Question
upstudy study bank question image url

Ask by Powers Robbins. in Paraguay
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

22) El límite es .
23) El límite es .

Solution

22) Sea
Al evaluar en , obtenemos en el numerador y en el denominador. Por lo tanto, se tiene la indeterminación .
Aplicamos la regla de L’Hôpital diferenciando el numerador y el denominador.
  • Derivada del numerador:
  • Derivada del denominador:
Entonces, el límite se transforma en:
Sustituyendo :
por lo que el límite es:
23) Sea
Al evaluar en , obtenemos:
lo que resulta en la indeterminación .
Aplicamos la regla de L’Hôpital diferenciando el numerador y el denominador respecto a .
  • Derivada del numerador:
  • Derivada del denominador:
El límite se convierte en:
Sustituyendo :
obtenemos:

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

To solve the first limit, we start by substituting in the expression . This results in an indeterminate form . To resolve this, we can use algebraic manipulation. By multiplying the numerator and the denominator by the conjugates, we can simplify the expression and ultimately find that the limit evaluates to 2.
For the second limit, we can set to obtain another indeterminate form . Here, we can apply L’Hôpital’s Rule or further algebraic simplifications. Working it through step-by-step using differentiation or rationalizing the radicals will lead us to find that the limit evaluates to 1, provided and are positive constants.

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy