Exam (elaborations)
Exámenes de cálculo
- Course
- Institution
Enunciados de exámenes sobre cálculo.
[Show more]
Seller
Follow
alejandrocomesaaalmuia
Content preview
E.E. TelecomunicaciónDepto de Matemática Aplicada II
Matemáticas: Cálculo I
10 de enero de 2018
APELLIDOS, NOMBRE, DNI:
GRUPO:
Evaluación continua: preguntas 4, 5 y 6.
Evaluación no continua: todas las preguntas.
1. Razona la verdad o falsedad de las siguientes afirmaciones:
e−x
a) La función f (x) = tiene dos extremos relativos.
x2
b) Sea f (x) = ln(x − 2) y sea p(x) su polinomio de Taylor de grado 3 centrado en x0 = 3.
Entonces p(7/2) = 5/12.
c) La función f (x) = 2x + (3x + 1)1/3 no tiene puntos de inflexión.
(2, 25 = 3 x 0.75 ptos. apartado)
2. Sea Ω la región de R3 dada por
Ω = {(x, y, z) ∈ R3 ; x2 + y 2 + z 2 ≤ 1 ; x2 + y 2 ≥ 1 − z ; x > 0 ; y > 0 ; z > 0}
a) Representa gráficamente Ω.
b) Expresa Ω en coordenadas cilı́ndricas.
(1, 25 ptos.)
3. Sea f : R2 → R definida por
x3 cos(y − 2)
si (x, y) 6= (0, 2)
x2 + (y − 2)2
f (x, y) =
0 si (x, y) = (0, 2)
a) Calcula D1 f (0, 2) y D2 f (0, 2).
b) Calcula D11 f (0, 2).
(1, 5 ptos.)
, 4. Sea f un campo escalar en R3 diferenciable. Se define F : R2 → R3 como
F (x, y) = (exy + y, xy 2 + 3x, f (y, 2x + y, x)).
a) Calcula DF (x, y) para todo (x, y) ∈ R2 .
~ (2, 2, 0) = (1, 3, 2), calcula la derivada de F en (0, 2) según el vector
b) Sabiendo que ∇f
u = (1, 1).
(1, 5 ptos.)
5. Sea F : R3 → R3 definida por:
F (x, y, z) = (F1 (x, y, z), F2 (x, y, z), F3 (x, y, z)) = (xexy +z 2 , cos(xz +y), x2 +yz +sen(xz +y)).
~ ( π , 0, 1).
Calcula divF ( π2 , 0, 1) y rotF 2
(1 pto.)
6. Sea f : R2 → R definida por f (x, y) = x2 + y 2 − xy + 3.
a) Calcula los extremos relativos de f y clasifı́calos.
b) Utilizando multiplicadores de Lagrange, calcula y clasifica los extremos relativos de f condi-
cionados por x2 + y 2 = 4 tales que x > 0.
(2, 5 ptos.)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller alejandrocomesaaalmuia. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.90. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81849 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now