Problem 1 :
continuous at x = -1 and continuous at x = 2 ?
Problem 2 :
continuous at x = 1 ?
Problem 3 :
Problem 4 :
Problem 5 :
The function f has the properties indicated in the table below. Which of the following must be true ?
a) f is continuous at x = 1 b) f is continuous at x = 2
c) f is continuous at x = 3 d) None of the above.
Problem 6 :
If the function f is continuous for all real numbers and if
f(x) = (x^{2} - 4)/(x + 2)
when x ≠ 2, then f(-2) =
A) -4 B) -2 C) -1 D) 0 E) 2
Problem 7 :
Let f be the function given above. What are all values of a and b for which f is differentiable at x = 2 ?
a) 1/4 and b = -1/2
b) a = 1/4 and b = 1/2
c) a = 1/4 and b is any real number]
d) a = b + 2 where b is any real number
e) There are no such values of a and b.
1) The function is continuous at x = -1.
The function is not continuous at x = 2.
2) So, the function g(x) is not continuous at x = 1.
3) The function is not continuous at x = -3 and continuous at x = 4.
4) So, the function f(x) is not continuous at x=π/2 and continuous at x = π.
5) lim_{ x->3}^{-} f(x) and lim_{ x->3}^{+} f(x) they are equal. So, the function f(x) is continuous at x --> 3, option c.
6) So, the answer is -4.
7) So, option a is correct.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM