Q2. Solve for x ?
if x[x] = 15 [x] Denotes the greatest integer less than or equal to x
if x[x] = 15 [x] Denotes the greatest integer less than or equal to x
Anonymous Quiz
36%
(A) 5
30%
(B) 3
12%
(C) 4
22%
(D) None of the above
If
Lim x→0 f(x) EXIST
That Means
Left Hand Limit (LHL) = Right Hand Limit(RHL) at x =0
LHL Means when x approaches from left hand side of zero on real number line or on x axis
In this case we assume that x is slightly less than ZERO(0)
LHL Represented by
LHL = x→0⁻ f(x)
RHL Means when x approaches from Right hand side of zero on real number line or on x axis
In this case we assume that x is slightly greater than ZERO(0)
RHL Represented by
RHL = x→0⁺ f(x)
NOTE 1
If
x→0⁻ f(x) = = x→0⁺ f(x)
in this case LIMIT WILL EXIST AT X =0
NOTE 2
If
x→0⁻ f(x) = = x→0⁺ f(x) = f(0)
f(0) = value of function at x =0
in this case FUNCTION f(x) WILL BE CONTINUOUS AT X =0
THANKS
Best Wishes
Lim x→0 f(x) EXIST
That Means
Left Hand Limit (LHL) = Right Hand Limit(RHL) at x =0
LHL Means when x approaches from left hand side of zero on real number line or on x axis
In this case we assume that x is slightly less than ZERO(0)
LHL Represented by
LHL = x→0⁻ f(x)
RHL Means when x approaches from Right hand side of zero on real number line or on x axis
In this case we assume that x is slightly greater than ZERO(0)
RHL Represented by
RHL = x→0⁺ f(x)
NOTE 1
If
x→0⁻ f(x) = = x→0⁺ f(x)
in this case LIMIT WILL EXIST AT X =0
NOTE 2
If
x→0⁻ f(x) = = x→0⁺ f(x) = f(0)
f(0) = value of function at x =0
in this case FUNCTION f(x) WILL BE CONTINUOUS AT X =0
THANKS
Best Wishes
Q3. Calculate the value of I
if I = [√1] + [√2] + [√3] .......[√100]
Where [ x ] Denotes greatest integer less than or equal to x.
if I = [√1] + [√2] + [√3] .......[√100]
Where [ x ] Denotes greatest integer less than or equal to x.
Anonymous Quiz
20%
(A) 615
30%
(B) 625
42%
(C) 5050
8%
(D) 505
Q4. Solve for x
If f₁(x) = f₂(x), Given
f₁(x) = [x/2] + [(x+1)/2] f₂(x) = [x/2022] + [(x+1)/2022] + [(x+2)/ 2022] + ............+ [(x+2021)/2022] Where [ ● ] Denotes Greatest Integer function less than or equal to x,
If f₁(x) = f₂(x), Given
f₁(x) = [x/2] + [(x+1)/2] f₂(x) = [x/2022] + [(x+1)/2022] + [(x+2)/ 2022] + ............+ [(x+2021)/2022] Where [ ● ] Denotes Greatest Integer function less than or equal to x,
Anonymous Quiz
12%
(A) x ∈ [0 ∞)
41%
(B) x ∈ (0 ∞)
42%
(C) x ∈ (-∞ ∞)
5%
(D) None of These
Q5.If D₁ is the domain of the function f₁(x) = √x² - [x] ² ) and D₂ is the domain of function f₂(x) = 1/f₁(x) calculate the value of D₁ ∩ D₂ ? Where Denotes greatest integer function less than or equal to x and Z denotes Integers【RADIUS JEE】
Anonymous Quiz
29%
(A) x ∈ (-∞ ∞)
46%
(B) x ∈ (-∞ ∞) - Z
19%
(C) x ∈ (0 ∞) - Z
6%
(D) None of the above
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Set representation method in Mathematics - RADIUS JEE
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Problems and Solution on Greatest Integer Function #5
Problems and Solution on Greatest Integer Function #5
*Content:*
*(1)* MCQ Based Problem on Greatest Integer Function.
*(2)* Method of sketching graph of Greatest Integer Function f(x) = [1 + 1/2(Sinx)]
*(3)* You will know How to Sketch the Graph of function…
*Content:*
*(1)* MCQ Based Problem on Greatest Integer Function.
*(2)* Method of sketching graph of Greatest Integer Function f(x) = [1 + 1/2(Sinx)]
*(3)* You will know How to Sketch the Graph of function…
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Problems and Solution on Greatest Integer Function #6
Problems and Solution on Greatest Integer Function #6
*Content:*
You will get the following listed Content in this RADIUS JEE video Lecture.
f(x) = [ x ] = Denotes Greatest Integer Function less than or equal to x
*(1)* MCQ Based Problem on Greatest Integer…
*Content:*
You will get the following listed Content in this RADIUS JEE video Lecture.
f(x) = [ x ] = Denotes Greatest Integer Function less than or equal to x
*(1)* MCQ Based Problem on Greatest Integer…
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Fractional Part Function Theory Class 1 | Know the Important Concepts
Fractional Part Function Theory Class 1 | Know the important concepts
*Content:*
You will get the following listed content in this RADIUS JEE video Lecture
*(1)* Definition of fractional part function f(x) = {x}
*(2)* Symbol of representation of fractional…
*Content:*
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*(1)* Definition of fractional part function f(x) = {x}
*(2)* Symbol of representation of fractional…
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Gratest Integer Function f(x)=[x]
Definition | Symbol of Representation | Domain | Range | Properties | Problems and Solution
Definition | Symbol of Representation | Domain | Range | Properties | Problems and Solution