1. Ans:(A) 123
Given function:
The derivative would be:
=>
=>
=>
Now at x = 7:
=>
2. Ans:(B) 3
Given function:
The derivative would be:
=>
=>
=>
Now at x = 4:
(as constant)
=>Ans:
3
3. Ans:(D) -5
Given function:
The derivative would be:
or
=>
=>
Now at x = -1:
=>
=> Ans:
4. Ans:(C) 7 divided by 9
Given function:
The derivative would be:
or
=>
=>
Now at x = -3:
=>
=> Ans:
5. Ans:(C) -8
Given function:
Now if we apply limit:
=>
=> Ans:
6. Ans:(C) 9
Given function:
Now if we apply limit:
=>
=> Ans:
7. Ans:(D) doesn't exist.
Given function:
In this case, even if we try to simplify it algebraically, there would ALWAYS be x power something (positive) in the denominator. And when we apply the limit approaches to 0, it would always be either + infinity or -infinity. Hence, Limit doesn't exist.
Check:
If you apply the limit, answer would be infinity.
8. Ans:(A) Doesn't Exist.
Given function:
Same as Question 7
If we try to simplify it algebraically, there would ALWAYS be x power something (positive) in the denominator. And when we apply the limit approaches to 0, it would always be either + infinity or -infinity. Hence, Limit doesn't exist.
9, 10.
Please attach the graphs. I shall amend the answer. :)
11. Ans:(A) Doesn't exist.
First We need to find out:
where,
If both sides are equal on applying limit then limit does exist.
Let check:
If x
9: answer would be 9+9 = 18
If x
9: answer would be 9-9 = 0
Since both are not equal, as
, hence
limit doesn't exist.
12. Ans:(B) Limit doesn't exist.
Find out:
where,
If all of above three are equal upon applying limit, then limit exists.
When x < 1 -> 1-1 = 0
When x = 1 -> 8
When x > 1 -> 7 + 1 = 8
ALL of the THREE must be equal. As they are not equal. 0
8; hence,
limit doesn't exist.
13. Ans:(D) -∞
; x = 9
f(x) = 1/(x-9).
Table:
x f(x)=1/(x-9)
----------------------------------------
8.9 -10
8.99 -100
8.999 -1000
8.9999 -10000
9.0 -∞
Below the graph is attached! As you can see in the graph that at x=9, the curve approaches but NEVER exactly touches the x=9 line. Also the curve is in downward direction when you approach from the left. Hence, -∞, x =9 (correct)
14. Ans: -6
s(t) = -2 - 6t
Inst. velocity = 
Therefore,
At t=2,
Inst. velocity = -6
15. Ans: +∞, x =7
f(x) = 1/(x-7)^2.
Table:
x f(x)= 1/(x-7)^2
--------------------------
6.9 +100
6.99 +10000
6.999 +1000000
6.9999 +100000000
7.0 +∞
Below the graph is attached! As you can see in the graph that at x=7, the curve approaches but NEVER exactly touches the x=7 line. The curve is in upward direction if approached from left or right. Hence, +∞, x =7 (correct)
-i
