Calculus

posted by .

If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true?
I. g(x) = 1 at least once
II. lim g(x) = g(3.5) as x aproaches 3.5.
III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches from the right

A. I only
B. II only
C. I and II only
D. I, II, and III
E. None of these.

I want to say that the answer should be D. I, II, and III since the function is continuous for all real numbers. Would this be correct?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    State which of the conditions are applicable to the graph of y = f(x). (Select all that apply.) lim x→infinity f(x) = −infinity lim x→a+ f(x) = L lim x→infinity f(x) = L f is continuous on [0, a] lim x→infinity …
  2. Calculus

    Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f?
  3. Calculus (Limits)

    If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true?
  4. Calculus (Limits)

    Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f?
  5. Calculus

    Suppose that f(x), f'(x), and f''(x) are continuous for all real numbers x, and the f has the following properties. I. f is negative on (-inf, 6) and positive on (6,inf). II. f is increasing on (-inf, 8) and positive on 8, inf). III. …
  6. Calculus, please check my answers!

    1. Evaluate: lim x->infinity(x^4-7x+9)/(4+5x+x^3) 0 1/4 1 4 ***The limit does not exist. 2. Evaluate: lim x->infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 ***2/3 The limit does not exist. 3. lim x->0 (x^3-7x+9)/(4^x+x^3) 0 1/4 1 ***9 …
  7. Check my CALCULUS work, please! :)

    Question 1. lim h->0(sqrt 49+h-7)/h = 14 1/14*** 0 7 -1/7 Question 2. lim x->infinity(12+x-3x^2)/(x^2-4)= -3*** -2 0 2 3 Question 3. lim x->infinity (5x^3+x^7)/(e^x)= infinity*** 0 -1 3 Question 4. Given that: x 6.8 6.9 6.99 …
  8. Calculus

    Let f be a function defined for all real numbers. Which of the following statements must be true about f?
  9. Calculus

    If the functions f and g are defined for all real numbers and f is an antiderative of g, which of the following statements is NOT necessarily true?
  10. Calculus

    If the functions f and g are defined for all real numbers and f is an antiderivative of g, which of the following statements is NOT necessarily true. (A)If g(x)>0 for all x, then f is increasing (B)If g(a)=0, then f(x) has a horizontal …

More Similar Questions