Let and . Discuss the continuity of ( ) and at…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

Y_n(x) = x^2 + \frac{x^2}{1+x^2} + \frac{x^2}{(1+x^2)^2} + \dots + \frac{x^2}{(1+x^2)^{n-1}}

and

Y(x) = \lim_{n \to \infty} Y_n(x)

. Discuss the continuity of

Y_n(x)

(

n = 1, 2, 3, \dots

) and

Y(x)

at

x = 0

.

Related theory

Browse the problem library