Let I be an open interval that contains the point c, let f and g be functions th

Question

Let I be an open interval that contains the point c, let f and g be functions that are defined on I except possibly at c, and suppose that g is a bounded function. Suppose that lim x->c f(x)=0. Prove that lim x->c (fg)(x)=0.

Explanation / Answer

lim x?a c = c. (Rule 1). Proof : Let ? > 0. In reference to the definition of limit, the function ... (1) lim x?a. (f(x) + g(x)) = lim x?a f(x) + lim x?a g(x);. (2) lim x?a. (cf(x)) = c lim x?a f(x);. (3) lim x?a ... Now suppose x is a number in the domains of both f and g such that. 0 < |x ? a| < ?. ..... 0 < |x ? a| < ? =?

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.