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Practice Exam Problems - EXAM #1, Exercises of Differential and Integral Calculus

The University of Texas at AustinDifferential and Integral Calculus
Prof. Oscar Gonzalez

Practice problems for the first exam in M408C for Prof. Oscar Gonzales.

Typology: Exercises

2023/2024

Uploaded on 10/17/2024

rdrd
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M408C Practice Problems Exam #1
multiple choice, one answer per problem
1. Suppose
lim
x→4+f(x) = 3,lim
x→4+g(x) = 2,
lim
x→4+h(x) = ∞,lim
x→4+j(x) = ∞.
Which limit is indeterminate (inconclusive)?
(A) lim
x→4+
f(x)
g(x).
(B) lim
x→4+h(x)−j(x).
(C) lim
x→4+
f(x)
j(x).
(D) lim
x→4+g(x)h(x).
(E) lim
x→4+f(x) + j(x).
pf3
pf4
pf5
pf8
pf9
pfa

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M408C Practice Problems Exam # multiple choice, one answer per problem

  1. Suppose xlim→ 4 +^ f^ (x) = 3,^ xlim→ 4 +^ g(x) = 2, x^ lim→ 4 +^ h(x) =^ ∞,^ xlim→ 4 +^ j(x) =^ ∞. Which limit is indeterminate (inconclusive)? (A) (^) xlim→ 4 +^ f g^ ((xx)). (B) (^) xlim→ 4 + h(x) − j(x). (C) (^) xlim→ 4 +^ f j^ ((xx) ). (D) (^) xlim→ 4 + g(x)h(x). (E) (^) xlim→ 4 + f (x) + j(x).
  1. The set of all x which satisfy | 2 x − 1 | ≤ 5 is: (A) (− 2 , 3). (B) (−∞, −2] ∪ [3, ∞). (C) [− 2 , ∞). (D) [− 2 , 3]. (E) (−∞, 3].
  1. If e^2 e^3 x^ = 4e^4 x, then x = (A) 1 − ln 6. (B) 4 + ln 2. (C) 2 − ln 4. (D) 3 − ln 2. (E) 2 − ln 8.
  1. (^) xlim→ (^0) x^ sin(2 (^2) + 6xx) =

(A)^23. (B)^16. (C) 0. (D)^13. (E) does not exist.

  1. (^) xlim→ 1 + x 2 x+ 2^2 −x^9 − 3 =

(A) 6. (B) −∞. (C) 3. (D) − 12. (E) ∞.

  1. (^) xlim→ 0 tan(4x) cot(6x) =

(A) does not exist. (B) − 32. (C) − 12 1. (D)^12. (E)^23.

  1. Consider y =^2 x + 2 as shown.

x

y 4 1

y = f(x)

Giventhat if ε| (^) x= − 12 1 find all values of| < δ then |y − 4 | δ >< ε (^) .0 so (A) δ =^15 (or smaller). (B) δ =^12 (or smaller). (C) δ =^14 (or smaller). (D) δ = 10 1 (or smaller). (E) δ = 20 1 (or smaller).

  1. If a > 0 is a constant, then lim x→a √^ xx^ −−^ a√a =

(A) does not exist. (B) a 2. (C) 2√a. (D)^ √ a^2. (E)^ √^ √a 2.