1. Ans:(A) 123
Given function: 

The derivative would be:

=> 

=> 

=> 

Now at x = 7:

=> 
 2. Ans:(B) 3
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
4. Ans:(C) 7 divided by 9
Given function: 

The derivative would be:

or 

=> 

=> 

Now at x = -3:

=> 

=> Ans: 
 5. Ans:(C) -8
5. Ans:(C) -8
Given function: 

Now if we apply limit:

=> 

=> Ans: 
 6. Ans:(C) 9
6. Ans:(C) 9
Given function: 

Now if we apply limit:

=> 

=> Ans: 
 7. Ans:(D) doesn't exist.
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