True or False
If f is differentiable everywhere and f^′(x)<0 for all x, then lim x→∞ f(x)= −∞
True or False If f is differentiable everywhere and f^′(x)<0 for all x, then lim x→∞ ...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
Let f(x) be a differentiable function with inverse of f(x) such that f(0)=0 and f'(0) is not 0. Prove lim(x->0) f(x)/f −1(x) =f'(0)^2 f-1(x) is f inverse of x
Suppose that fn(x) converges to f(x) uniformly, that the functions fn(x) are all differentiable, and that the function f(x) is also differentiable. (All of these conditions are assumed to be true on a bounded, closed interval [a, b].) Prove or disprove: lim as n goes to infinity fn'(x) = f'(x)
True or False: If f(x) and g(x) are two differentiable functions on an interval (a,b), and f(x)>g(x) on (a,b), then f'(x)>g'(x).
5. 5 Let f(x) be continuous and differentiable on f(5) = 4. Mark TRUE or FALSE for the following statements and JUSTIFY. (No points will be given without the correct justification) [0, 10] with f(0) = f(10) 0 and (E) There is some c E (0,5) such that f'(c) = 5. 5 Let f(x) be continuous and differentiable on f(5) = 4. Mark TRUE or FALSE for the following statements and JUSTIFY. (No points will be given without the correct...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
3. Given that lim f(x) = 4 and lim f(x) = -4, what is true about lim f(x)? x-1 4. Given that lim f(x) = 1, lim f(x) = 1, and f(-3) = 1, what is true about lim f(x)? 5. Given that lim f(x) = 0, lim f(x) = 0, and f(2) = 3, what is true about limf(x)? X-3 X-3 X-2
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint: Use the definition of derivative and then use mean value theorem) 2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) =...
homework help true or false question. TRUE OR FALSE 5. If f is differentiable on R, f(1) = 8, and f(15) = 10, then there is a number c for which f'(c) = 7
1. (3 points each) Answer each of the following statements as true or false a. If lim ) exists, then lim(lim() b. If lim f (x) exists, then fi (zo) exists. c. If f differentiable on la, b, then f is integrable on [a, b]. d. If f is continuous on [a, b] and differentiable on (a, b), then there exists a number X -To (a, b) such that f (b) f(a)- (b-a)f (x). e. If f is integrable on...