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 g(x) = lim_(nto oo) y_(n)(x)`, then `y_(n)(x), n = 1, 2, 3,...,n and y(x)` is

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 Exercise (Questions Asked In Previous 13 Years Exam)|43 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_(x rarr oo)y_(n)(x) Discuss the continuity of y_(n)(x)(n=1,2,3dots n) and y(x)atx=0

If y=1+x+(x^(2))/(2!)+(x^(3))/(3!)...(x^(n))/(n!)

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). ... + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n))) is equal to lim_ (n rarr oo) sum_ (n = 1) ^ (n) (1 ) / (2 ^ (n)) tan ((x) / (2 ^ (n)))

Simplify : (x^(2^(n-1)) + y^(2^(n-1)))(x^(2^(n-1)) - y^(2^(n-1)))

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

If y=cos^(-1)((x^(2n)-1)/(x^(2n)+1)))," then "(1+x^(2n))y_(1)=

Let f(x)=x+(1-x)x^(2)+(1-x)(1-x^(2))x^(3)+............+(1-x)(1-x^(2)).........(1-x^(n-1))x^(n);(n) then :

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

Let f:[0,1]vec[0,1] be a continuous function. Then prove that f(x)=x f...
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))+...+(x...
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
|
Let f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(2)).sin^(-1)(1-{x}))/(sqrt(2)...
Text Solution
|
Let f(x) = {{:(sgn(x)+x",",-oo lt x lt 0),(-1+sin x",",0 le x le pi//2...
Text Solution
|
Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If...
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
|
If f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(...
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
|
f(x)=(cosx-sin2x)/((pi-2x)^2);g(x)=(e^(-cosx)-1)/(8x-4pi)
Text Solution
|