True/ False Calc Final
(c) True or False: If f is continuous on the closed interval [0, 5], then f is continuous at every point in [0, 5].
false
(c) True or False: If limx→c f(x) = 10, then f(c) = 10.
false
(c) True or False: When using L'Hopital's rule, you needˆ to apply the quotient rule in the differentiation step.
false
(d) True or False: (3x + 1)^k = k(3x + 1)^(k−1)
false
(d) True or False: Every algebraic function f is continuous at every real number x = c.
false
(d) True or False: If f is continuous on the interval (2, 4), then f must have a maximum value and a minimum value on (2, 4).
false
(d) True or False: If f(c) = 10, then limx→c f(x) = 10.
false
(d) True or False: L'Hopital's rule applies only to limits asˆ x→0 or as x→ ∞.
false
(d) True or False: The two-sided limit of f(x) as x→c exists if and only if the left and right limits of f(x) exist as x→c.
false
(e) True or False: 1/x^3'=1/3x^2
false
(e) True or False: A function can approach more than one limit as x approaches c.
false
(e) True or False: If f is any function with f(2) = 0 and f(8) = 0, then there is some c in the interval (2, 8) such that f'(c) = 0.
false
(e) True or False: If f(3) = −5 and f(9) = −2, then there must be a value c at which f(c) = −3.
false
(e) True or False: If the graph of f has a vertical asymptote at x = 5, then lim x→5 f(x) = ∞.
false
(f) True or False: If f is continuous everywhere, and if f(−2) = 3 and f(1) = 2, then f(x) must have a root somewhere in (−2, 1).
false
(f) True or False: If f'(1) = 0 and f''(1) = −2, then f has a local minimum at x = 1.
false
(f) True or False: If lim x→2 ln( f(x)) = 4, then lim x→2
false
(f) True or False: If lim x→4 f(x) = 10, then we can make f(x) as close to 4 as we like by choosing values of x sufficiently close to 10.
false
(f) True or False: The function f(x) = sec x is continuous at x =π/2
false
(g) True or False: If f is continuous and differentiable on [0, 10] with f'(5) = 0, then f has a local maximum or minimum at x = 5.
false
(g) True or False: If lim x→2 f(x) = ∞, then the graph of f has a horizontal asymptote at x = 2.
false
(g) True or False: The second-derivative test involves checking the sign of the second derivative on each side of every critical point.
false
(g) True or False: The value of (x−c)f(x)/ (x−c)g(x) at x = c is equal to the limit of f(x)/g(x) at x = c.
false
(h) True or False: If f is continuous and differentiable on [0, 10] with f'(5) = 0, then there are some values a and b in (0, 10) for which f(a) = 0 and f(b) = 0.
false
(h) True or False: If f(0) = f(6) = 0 and f(2) > 0, then f(x) is positive on the entire interval (0, 6).
false
(h) True or False: If lim x→2 ln( f(x)) = −∞, then lim x→2 f(x) = −∞.
false9
(h) True or False: The second-derivative test always produces exactly the same information as the first-derivative test.
false9
(b) True or False: The limit of f(x) as x→c is the value f(c).
false
(b) True or False: We can calculate a limit of the form limx→c f(x) simply by finding f(c).
false
(c) True or False: If f is concave up on an interval I, then f''' is positive on I.
false
(b) True or False: If f'''is concave up on an interval I, then it is positive on I.
false
(b) True or False: L'Hopital's rule can be used to find theˆ limit of any quotient f(x)/g(x) as x→c.
false
(a) True or False: For limx→c f(x) to be defined, the function f must be defined at x = c.
false
(a) True or False: If a limit has an indeterminate form, then that limit does not have a real number as its solution.
false
(a) True or False: If f'''(2) = 0, then x = 2 is an inflection point of f .
false
(b) True or False: (ks + r)' = k.
false
(a) True or False: (5)' = 0.
true
(a) True or False: A limit exists if there is some real number that it is equal to.
true
(a) True or False: If f is both left and right continuous at x = c, then f is continuous at x = c.
true
(a) True or False: Rolle's Theorem is a special case of the Mean Value Theorem.
true
(a) True or False: The limit of a difference of functions as x→c is equal to the difference of the limits of those functions as x→c, provided that all limits involved exist.
true
(b) True or False: If f is continuous on the open interval (0, 5), then f is continuous at every point in (0, 5).
true
(b) True or False: The Mean Value Theorem is so named because it concerns the average (or "mean") rate of change of a function on an interval.
true
(c) True or False: (ks + r)' = k.
true
(c) True or False: If f is differentiable on R and has an extremum at x = −2, then f'(−2) = 0.
true
(c) True or False: The limit of f(x) as x→c might exist even if the value f(c) does not.
true
(d) True or False: If f has a critical point at x = 1, then f has a local minimum or maximum at x = 1.
true
(d) True or False: If f'''(2) does not exist and x = 2 is in the domain of f , then x = 2 is a critical point of the function f'
true
(e) True or False: Every power function f(x) = Ax k is continuous at the point x = 2.
true
(e) True or False: If f has an inflection point at x = 3 and f is differentiable at x = 3, then the derivative f' has a local minimum or maximum at x = 3.
true
(e) True or False: L'Hopital's rule applies only to limits ofˆ the indeterminate form 0/0 or ∞/∞
true
(f) True or False: If f is continuous and differentiable on [−2, 2] with f(−2) = 4 and f(2) = 0, then there is some c∈(−2, 2) with f'(c) = −1.
true
(f) True or False: If lim x→5 f(x) = ∞, then the graph of f has a vertical asymptote at x = 5.
true
(g) True or False: If f is continuous everywhere, and if f(0) = −2 and f(4) = 3, then f(x) must have a root somewhere in (0, 4).
true
(g) True or False: If lim x→6 f(x) = ∞, then we can make f(x) as large as we like by choosing values of x sufficiently close to 6.
true
(h) True or False: The limit of (x−c)f(x)/(x−c)g(x) as x→c is equal to the limit of f(x)/g(x) as x→c.8
true
f(x) =ln 4. (g) True or False: If lim x→2 ln( f(x)) = ∞, then lim x→2 f(x) = ∞.
true
(h) True or False: If lim x→−∞ f(x) = 2, then the graph of f has a horizontal asymptote at y = 2.
true9
and 100.1 by choosing values of x that are sufficiently large.
true9