If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1...

If `Isum_(k=1)^(98)int_k^(k+1)(k+1)/(x(x+1))dx ,t h e n:` (a) `I<(49)/(50)` (b) `I >(log)_e 99` (c) `I >(49)/(50)` (d) `I<(log)_e 99`

A

`I gt log_(e) 99`

B

`I lt log_(o) 99`

C

`I lt (49)/(50)`

D

`I gt (49)/(50)`

Text Solution

Verified by Experts

The correct Answer is:

BD

Topper's Solved these Questions

DEFINITE INTEGRATION & ITS APPLICATION
RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos
DEFINITE INTEGRATION & ITS APPLICATION
RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
DEFINITE INTEGRATION & ITS APPLICATION
RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos
COMBINATORICS
RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos
DPP
RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

S=sum_(i=1)^nsum_(j=1)^isum_(k=1)^j1

If sum_(k=0)^(200)i^k+prod_(p=1)^(50)i^p =x+iy then (x,y) is

The value of int_0^1lim_(n->oo)sum_(k =0)^n(x^(k+2)2^k)/(k!)dx is: (a) e ^(2) -1 (b) 2 (c) (e ^(2)-1)/(2) (d) (e ^(2) -1)/(4)

The value of integral sum _(k=1)^(n) int _(0)^(1) f(k - 1+x) dx is

If I_(n)=int_(0)^(pi) e^(x)sin^(n)x " dx then " (I_(3))/(I_(1)) is equal to

If f(x)=(e^x)/(1+e^x), I_1=int_(f(-a))^(f(a))xg(x(1-x)dx and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx , then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is (a) "^(n)C_(k)*3^(k) (b) "^(n+1)C_(k)*3^(k) (c) "^(n+1)C_(k)*3^(k-1) (d) "^(n)C_(k-1)*3^(k)

If int_(0)^(1) cot^(-1)(1-x+x^(2))dx=k int_(0)^(1) tan^(-1)x dx , then k=

If I_(m)=int_(0)^(oo) e^(-x)x^(n-1)dx, "then" int_(0)^(oo) e^(-lambdax) x^(n-1)dx

"I f"I_1=int_(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I_2=int_(-100)^(101)(dx)/(5+2x-2x^2),t h e n(I_1)/(I_2)"i s" (a)2 (b) 1/2 (c) 1 (d) -1/2

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I

Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...
Text Solution
|
If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...
Text Solution
|
Let f: R rarr R be a continuous odd function, which vanishes exactly a...
Text Solution
|
Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...
Text Solution
|
Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...
Text Solution
|
The option(s) with the values of aa n dL that satisfy the following eq...
Text Solution
|
Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...
Text Solution
|
Let F : R to R be a thrice differentiable function . Suppose that F(...
Text Solution
|
Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...
Text Solution
|
The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...
Text Solution
|
Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx
Text Solution
|
Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...
Text Solution
|
Let f:Rto(0,1) be a continuous function. Then, which of the following ...
Text Solution
|
Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=...
Text Solution
|
If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: (a) I<(49)/(50...
Text Solution
|
If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...
Text Solution
|
If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(...
Text Solution
|
For each positive integer n let y(n)=1/n((n+1)(n+2)…..(n+n)^(1//n))....
Text Solution
|
A farmer F(1) has a land in the shape of a triangle with vertices at P...
Text Solution
|
The value of the integral int(0)^(1//2)(1+sqrt(3))/(((x+1)^(2)(1-x)^(6...
Text Solution
|