Concept explainers
Infinite limit proof Give a formal proof that
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Precalculus (10th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus and Its Applications (11th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- (Term-by-term Differentiability Theorem). Let fn be differentiable functions defined on an interval A, and assume ∞ n=1 fn(x) converges uniformly to a limit g(x) on A. If there exists a point x0 ∈ [a, b] where ∞ n=1 fn(x0) converges, then the series ∞ n=1 fn(x) converges uniformly to a differentiable function f(x) satisfying f(x) = g(x) on A. In other words, Proof. Apply the stronger form of the Differentiable Limit Theorem (Theorem6.3.3) to the partial sums sk = f1 + f2 + · · · + fk. Observe that Theorem 5.2.4 implies that sk = f1 + f2 + · · · + fk . In the vocabulary of infinite series, the Cauchy Criterion takes the followingform.arrow_forward(INFINITE SEQUENCE) Determine the convergence or divergence of the following sequences. If it converges give it its limit.arrow_forwardContinuity and the properties of limits: show a function is continuous at aarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage