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

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

Typology: Exercises

2023/2024

Uploaded on 10/17/2024

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M408C Practice Problems Exam #1
multiple choice, one answer per problem
1. Suppose
lim
x4+f(x) = 3,lim
x4+g(x) = 2,
lim
x4+h(x) = ,lim
x4+j(x) = .
Which limit is indeterminate (inconclusive)?
(A) lim
x4+
f(x)
g(x).
(B) lim
x4+h(x)j(x).
(C) lim
x4+
f(x)
j(x).
(D) lim
x4+g(x)h(x).
(E) lim
x4+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.