Question 1(multiple choice worth 6 points)
find the derivative of f(x) = -10x2 + 4x at x = 11.
-216
-196
-176
-363

question 2(multiple choice worth 6 points)
find the limit of the function by using direct substitution.
limit as x approaches four of quantity x squared plus three x minus one
does not exist
-27
0
27

question 3(multiple choice worth 6 points)
find the derivative of f(x) = 7x + 9 at x = 6.
7
9
6
0

question 4(multiple choice worth 7 points)
find the indicated limit, if it exists.
limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus 7 when x is greater than 0
3
10
7
the limit does not exist.

question 5(multiple choice worth 6 points)
find the derivative of f(x) = 3 divided by x at x = 1.
-3
-1
1
3

question 6(multiple choice worth 7 points)
use the given graph to determine the limit, if it exists.
a coordinate graph is shown with a horizontal line crossing the y axis at four that ends at the open point 2, 4, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3.
find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
-3; 4
1; 1
4; -3
does not exist; does not exist

question 7(multiple choice worth 7 points)
find the indicated limit, if it exists.
limit of f of x as x approaches negative 1 where f of x equals x plus 1 when x is less than negative 1 and f of x equals 1 minus x when x is greater than or equal to negative 1
-1
2
the limit does not exist.
0

question 8(multiple choice worth 7 points)
use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 7 as x approaches 7 from the left.
-∞ ; x = 7
∞ ; x = -7
-∞ ; x = -7
1 ; no vertical asymptotes

question 9(multiple choice worth 7 points)
use the given graph to determine the limit, if it exists.
a coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1.5, a closed point at 3, 7, and a horizontal line starting at the open point 3, 2.
find limit as x approaches three from the left of f of x..
7
1.5
does not exist
2

question 10(multiple choice worth 6 points)
find the limit of the function algebraically.
limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.
0
-9
does not exist
9

question 11(multiple choice worth 6 points)
find the derivative of f(x) = negative 3 divided by x at x = -4.
3 divided by 4
3 divided by 16
16 divided by 3
4 divided by 3

question 12(multiple choice worth 6 points)
find the limit of the function by using direct substitution.
limit as x approaches zero of quantity x squared minus two.
2
-2
does not exist
0

question 13(multiple choice worth 6 points)
find the limit of the function algebraically.
limit as x approaches four of quantity x squared minus sixteen divided by quantity x minus four.
does not exist
4
1
8

question 14 (essay worth 9 points)
the position of an object at time t is given by s(t) = -1 - 13t. find the instantaneous velocity at t = 8 by finding the derivative.

question 15 (essay worth 8 points) use graphs and tables to find the limit and identify any vertical asymptotes of the function. limit of 1 divided by the quantity x minus 2 squared as x approaches 2

ANSWER TO QUESTION 1

The given function is . We want to find the derivative of this function at .

The derivative of this function is given by,

We now have to substitute   in to   to obtain,

This implies that,

Ans: A

ANSWER TO Q2.

The given limit is .

The function whose limit we are finding is a polynomial function. Since polynomial function are continuous everywhere, the limiting value is always equal to the functional value.

Thus,

This implies that,

Thus, .

Ans: A.

ANSWER TO Q3

The given function is .

We want to find the derivative of this function at .

We must first of all differentiate this function to obtain,

We can see that the derived function is constant, therefore value of will still give us

This implies that,

Ans: A

ANSWER TO Q4.

See attachment

ANSWER TO Q5.

The given function is .

To find the derivative of this function at,

, we must first differentiate this function.

But let us rewrite the rational function as a power function so that it will be easier to differentiate using the power rule of differentiation.

That is,

.

We differentiate now to obtain,

This implies that,

At

Ans: A

ANSWER TO Q6

The graph that has been described in the question is shown in the diagram above,

We can see from the graph that as we approach , from the left, the y-values are approaching .

That is,

Also as we approach from the right, the y-values are approaching .

That is,

.

Ans: D.

ANSWER TO Q7

The given piece-wise function is

Since

We evaluate the limit at of .

Since this is a polynomial function,

This implies that,

Ans: B.

ANSWER TO Q8

The given function is .

This is a rational function that is defined for all real values except,

Therefore the vertical asymptote is

We can see from the graph above that, as x approaches seven from the left, the function approaches negative infinity

That is .

Ans: A.

ANSWER TO Q9

The graph of the given piece-wise function is show as follows;

We can see from the graph that, as the x-values are approaching 3 from the left y-values are approaching .

Note the limit is not the same as the functional value in this case. Also limit in this case is the y-value we are approaching as we get closer and closer to 3, not necessarily at 3.

See graph

Ans: B

ANSWER TO Q10

The given function is

We want to find the limiting value of this function as the x-values approaches zero.

Thus,

Since the function is not defined at .

We evaluate the one-sided limits as follows,

Since the right hand limit is not equal to the left hand limit,

Does Not Exist.

ANS: C

ANSWER TO Q11

The given function is

To find the derivative of this function at,

, we must first differentiate this function.

But let us rewrite the rational function as a power function so that it will be easier to differentiate using the power rule of differentiation.

That is,

.

We differentiate now to obtain,

This implies that,

At

Ans: B

ANSWER TO Q12

We want to find the limit of the function as x approaches zero.

This is a polynomial function, therefore

Ans: B

SEE  ATTACHMENT FOR ANSWER TO  QUESTIONS

13, 14 and 15

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".