RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Limits

 Page 1


29. Limits
Exercise 29.1
1. Question
Show that  does not exist.
Answer
Given
f(x) = 
f(x) = 
To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
 (from 2)
Thus, limit does not exist.
2. Question
Find k so that  may exist, where .
Answer
Given f(x) = 
To find 
To limit to exist, we know  …….(1)
thus 
From (1)
Page 2


29. Limits
Exercise 29.1
1. Question
Show that  does not exist.
Answer
Given
f(x) = 
f(x) = 
To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
 (from 2)
Thus, limit does not exist.
2. Question
Find k so that  may exist, where .
Answer
Given f(x) = 
To find 
To limit to exist, we know  …….(1)
thus 
From (1)
2(2 + 0) + 3 = (2 - 0) + k
4 + 3 = 2 + k
5 = k
3. Question
Show that  does not exist.
Answer
To find 
To limit to exist, we know  …….(1)
Thus, to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
4. Question
Let f(x) be a function defined by .
Show that  does not exist.
Answer
Given f(x) = 
f(x) = 
f(x) = 
To find 
Page 3


29. Limits
Exercise 29.1
1. Question
Show that  does not exist.
Answer
Given
f(x) = 
f(x) = 
To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
 (from 2)
Thus, limit does not exist.
2. Question
Find k so that  may exist, where .
Answer
Given f(x) = 
To find 
To limit to exist, we know  …….(1)
thus 
From (1)
2(2 + 0) + 3 = (2 - 0) + k
4 + 3 = 2 + k
5 = k
3. Question
Show that  does not exist.
Answer
To find 
To limit to exist, we know  …….(1)
Thus, to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
4. Question
Let f(x) be a function defined by .
Show that  does not exist.
Answer
Given f(x) = 
f(x) = 
f(x) = 
To find 
To limit to exist we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
5. Question
Let  . Prove that  does not exist.
Answer
Given f(x) = 
To find whether  exists?
To limit to exist we know  …….(1)
Thus to limit to exist ……(2)
From above equations
Thus, the limit  does not exists.
6. Question
Let . Prove that  does not exist.
Answer
Given f(x) = 
To find whether  exists?
To limit to exist we know  …….(1)
Thus to limit to exist ……(2)
Page 4


29. Limits
Exercise 29.1
1. Question
Show that  does not exist.
Answer
Given
f(x) = 
f(x) = 
To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
 (from 2)
Thus, limit does not exist.
2. Question
Find k so that  may exist, where .
Answer
Given f(x) = 
To find 
To limit to exist, we know  …….(1)
thus 
From (1)
2(2 + 0) + 3 = (2 - 0) + k
4 + 3 = 2 + k
5 = k
3. Question
Show that  does not exist.
Answer
To find 
To limit to exist, we know  …….(1)
Thus, to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
4. Question
Let f(x) be a function defined by .
Show that  does not exist.
Answer
Given f(x) = 
f(x) = 
f(x) = 
To find 
To limit to exist we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
5. Question
Let  . Prove that  does not exist.
Answer
Given f(x) = 
To find whether  exists?
To limit to exist we know  …….(1)
Thus to limit to exist ……(2)
From above equations
Thus, the limit  does not exists.
6. Question
Let . Prove that  does not exist.
Answer
Given f(x) = 
To find whether  exists?
To limit to exist we know  …….(1)
Thus to limit to exist ……(2)
From above equations
Thus, the limit  does not exists.
7. Question
Find , where
Answer
Given f(x) = 
To find 
To limit to exist we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus from (2),(3) and (4)
8. Question
If . Find and .
Answer
Given f(x) = 
(i)To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
Page 5


29. Limits
Exercise 29.1
1. Question
Show that  does not exist.
Answer
Given
f(x) = 
f(x) = 
To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
 (from 2)
Thus, limit does not exist.
2. Question
Find k so that  may exist, where .
Answer
Given f(x) = 
To find 
To limit to exist, we know  …….(1)
thus 
From (1)
2(2 + 0) + 3 = (2 - 0) + k
4 + 3 = 2 + k
5 = k
3. Question
Show that  does not exist.
Answer
To find 
To limit to exist, we know  …….(1)
Thus, to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
4. Question
Let f(x) be a function defined by .
Show that  does not exist.
Answer
Given f(x) = 
f(x) = 
f(x) = 
To find 
To limit to exist we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus, limit does not exist.
5. Question
Let  . Prove that  does not exist.
Answer
Given f(x) = 
To find whether  exists?
To limit to exist we know  …….(1)
Thus to limit to exist ……(2)
From above equations
Thus, the limit  does not exists.
6. Question
Let . Prove that  does not exist.
Answer
Given f(x) = 
To find whether  exists?
To limit to exist we know  …….(1)
Thus to limit to exist ……(2)
From above equations
Thus, the limit  does not exists.
7. Question
Find , where
Answer
Given f(x) = 
To find 
To limit to exist we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus from (2),(3) and (4)
8. Question
If . Find and .
Answer
Given f(x) = 
(i)To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
…….(5)
From above equations
 thus the limit exists
Thus from (5)
(ii) To find 
To limit to exist, we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
Thus from (2),(3) and (4)
9. Question
Find , if .
Answer
Given f(x) = 
To find 
To limit to exist we know  …….(1)
Thus to find the limit using the concept ……(2)
……..(3)
……(4)
From above equations
 thus the limit does not exists
10. Question
Evaluate , where