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- (5) Let f: (a, ∞) → R be such that lim xf(x) = L, LE R. Prove that lim f(x) = 0. x →∞ x →∞arrow_forwardA function f is said to be [Select] A function f is said to be [Select] < at x = cif lim f(x) = f(c). x+c+ ✓at x =c if lim f(x) = f(c). xCarrow_forwardDefinition 1. Let ACR and c be a limit point of A. Let f: A → R be a function. We say that lim f(x) = ∞ if for all M>0 there exists > 0 I-C so that for all x & A, if 0 M. (a) Prove that lim 2-0 = ∞. (b) Construct a definition of what "lim f(x) = L" means. Prove that I→∞ lim = 0. 14x (c) What should " lim f(x) = ∞" mean? Give an example of a function x →∞ where this holds.arrow_forward
- |x-1| If f (x) = , then lim f(x), lim f(x) and lim f (x) are... respectively x→1+ х—1 x→1- x→1 |x-1| Jika f (x) = , maka lim f(x), lim f(x) dan lim f (x) secara berturut-turut adalah... х-1 x→1+ x→1 1. O 1,-1, tidak ada (does not exist) 2. О -1, -1, -1 3. О 1, 1, 1 4. O -1, 1, tidak ada (does not exist)arrow_forward6. Evaluate lim F(x), where f is defined by F(x) =(picture)arrow_forwardAsap handwritten solution acceptable Urgentarrow_forward
- 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?arrow_forwardO Using the e- - definition of the limit, prove that if f and g are real valued functions such that lim f(x) = 3 and lim g(x) = 4 x→a HIG then lim (f(x) + g(x)) = 7. x-aarrow_forwardXー1 Question No1: Evaluate the limit limx-1i+g=3arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage