Let y(n)(x) = x^(2) + (x^(2))/(1+x^(2))+...

Let `y_(n)(x) = x^(2) + (x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+......(x^(2))/((1+x^(2))^(n-1))and y(x) = underset(n rarr oo)(lim) y_(n) (x)`. Discuss the continuity of `y_(n)(x)(n = 1, 2, 3....n) and y(x) "at x" = 0`

continuous for `x in R`

continuous for `x in R - {0}`

continuous for `x in R - {1}`

data unsufficient

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos
COMPLEX NUMBERS
ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos
COORDINATE SYSTEM AND COORDINATES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let y_(n)(x) = x^(2) + (x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+......(x^(2))/((1+x^(2))^(n-1))and y(x) = lim_(n rarr oo) y_(n) (x) . Discuss the continuity of y_(n)(x)(n = 1, 2, 3....n) and y(x) "at x" = 0

Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3) .

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+ . . .+(x^(n))/(n!) , prove that (dy)/(dx)+(x^(n))/(n!)=y

Letf(x) = lim_( n to oo) (x^(n)-sin x^(n))/(x^(n)+sin x^(n)) " for" xgt 0, x ne 1,and f(1)=0 Discuss the continuity at x=1.

In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N ,

Discuss the continuity of f(x)in[0,2],w h e r ef(x)=(lim)_(n->oo)(sin (pix/2))^(2n)

Discuss the continuity of the function f(x)=lim_(xto oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)) at x=1.

If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)

Let f:[0,1]to[0,1] be a continuous function. Then prove that f(x)=x fo...
Text Solution
|
If f(x) = (x + 1)/(x-1) and g(x) = (1)/(x-2), then (fog)(x) is discont...
Text Solution
|
Let y(n)(x) = x^(2) + (x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+.........
Text Solution
|
If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0 ((2a)^x-xlog(2a)-1)/(x^2), x...
Text Solution
|
Find dy/dx if y=(pi)/2-sinx
Text Solution
|
Find dy/dx if y= sin2x - x^3
Text Solution
|
Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1....a x^2+b\ \ \ \ \ \ \ \ for\...
Text Solution
|
If f(x) = {{:(A+Bx^(2)",",x lt 1),(3Ax - B+2",",x ge 1):}, then A and ...
Text Solution
|
If f(x) = {{:(|x-1|([x]-x)",",x ne 1),(0",",x = 1):}, then
Text Solution
|
If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):}, where [.] an...
Text Solution
|
If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):}, then g(x)...
Text Solution
|
Find dy/dx if y= x sinx
Text Solution
|
Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...
Text Solution
|
Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists an...
Text Solution
|
A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...
Text Solution
|
If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...
Text Solution
|
Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...
Text Solution
|
For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...
Text Solution
|
Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...
Text Solution
|
Find dy/dx if y=2x^7
Text Solution
|