(1) Ans: Option (B) -69

Given function:

The derivative of f(x) with respect to x is:

--- (1)

Plug the value of x = 10 in (1)

(1) =>

Hence the correct answer is Option (B) -69

(2) Ans: Option (C) 8

Given function:

The derivative of f(x) with respect to x is:

--- (1)

Plug the value of x = 9 in (1)

(1) =>

Hence the correct answer is Option (C) 8

(3) Ans: Option (B) -1.

Given function:

The derivative of f(x) with respect to x is:

At x = 2:

Hence the correct answer is Option (B) -1.

(4) Ans: Option (C) 9 divided by 16.

Given function:

The derivative of f(x) with respect to x is:

At x = -4:

Hence the correct answer is Option (C) 9 divided by 16.

(5) Ans: Option (D) 5

Given function:

Now apply the limit:

The correct answer is Option (D) 5.

(6) Ans: Option (D) 27

Given function:

Apply the limit:

The correct option is (D) 27

(7) Ans: Option (D) 8.

Given function:

Now apply limit:

The correct option is (D) 8.

(8) Ans: Option (A) Does not exist.

Given function:

Apply limit:

The correct answer is (A) Does not exist.

(9),(10)

Please attach the graphs! Thanks! :)

(11) Ans: limit doesn't exist (Option C)

Given function:

If both sides are equal on applying limit then limit does exist.

Let check:

If x<-1: answer would be -1+1 = 0

If x≥-1: answer would be 1-(-1) =2

Since both are not equal, as 0≠2, hence limit doesn't exist (Option C).

(12) Ans: Option (B) 7.

Given function:

If all of above three are equal upon applying limit, then limit exists.

When x < 0 -> 7-(0)^2 = 7

When x = 0 -> 7

When x > 0 -> -10(0) + 7 = 7

ALL of the THREE must be equal. As they are equal. Hence the correct option is (B) 7.

(13) Ans: -∞, x =3 (Option C)

Given function:

f(x) = 1/(x-3).

Table:

x f(x)=1/(x-3)

----------------------------------------

2.9 -10

2.99 -100

2.999 -1000

2.9999 -10000

3.0 -∞

Below the graph is attached! As you can see in the graph that at x=3, the curve approaches but NEVER exactly touches the x=3 line. Also the curve is in downward direction when you approach from the left. Hence, -∞, x =3 (Option C)

(14) Ans: Inst. velocity = -13

Given function:

s(t) = -1 -13t

Instantaneous velocity =

Therefore,

At t=8:

Inst. velocity = -13

(15) Ans: +∞, x =1

Given function:

f(x) = 1/(x-1)^2

Table:

x f(x)= 1/(x-1)^2

----------------------------------

0.9 +100

0.99 +10000

0.999 +1000000

0.9999 +100000000

1.0 +∞

Below the graph is attached! As you can see in the graph that at x=1, the curve approaches but NEVER exactly touches the x=1 line. The curve is in upward direction if approached from left or right. Hence, the correct answer is: +∞, x =1