7. Let f,g: R → R, and c Є R. 1. Prove: if both lim f(x) and lim(f + g)(x) exist in R, then lim g(x) exists in R. х-с x c x c 2. If lim f(x) and lim(fg)(x) exist in R, is that true lim g(x) exists in R? Show your x c argument. x c х-с
7. Let f,g: R → R, and c Є R. 1. Prove: if both lim f(x) and lim(f + g)(x) exist in R, then lim g(x) exists in R. х-с x c x c 2. If lim f(x) and lim(fg)(x) exist in R, is that true lim g(x) exists in R? Show your x c argument. x c х-с
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.4: Cicumference And Area Of A Cicle
Problem 21E: Let N be any point on side BC of the right triangle ABC. Find the upper and lower limits for the...
Question
Transcribed Image Text:7. Let f,g: R → R, and c Є R.
1. Prove: if both lim f(x) and lim(f + g)(x) exist in R, then lim g(x) exists in R.
х-с
x c
x c
2. If lim f(x) and lim(fg)(x) exist in R, is that true lim g(x) exists in R? Show your
x c
argument.
x c
х-с
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Similar questions
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage