limits calculus

1. Find the derivative of f(x) = 11x2 + 5x at x = 9. (6 points)
243
223
203
-243
2. Find the derivative of f(x) = 9x + 5 at x = 7. (6 points)
0
5
7
9
3. Find the derivative of f(x) = 4 divided by x at x = 2. (6 points)
-4
-1
1
4
4. Find the derivative of f(x) = negative 9 divided by x at x = -4. (6 points)
4 divided by 9
16 divided by 9
9 divided by 16
9 divided by 4
5. Find the limit of the function by using direct substitution. (6 points)

limit as x approaches zero of quantity x squared minus three.
3
Does not exist
-3
0
6. Find the limit of the function by using direct substitution. (6 points)

limit as x approaches four of quantity x squared plus three x minus one
Does not exist
-27
0
27
7. Find the limit of the function algebraically. (6 points)

limit as x approaches four of quantity x squared minus sixteen divided by quantity x minus four.
Does not exist
4
1
8
8. Find the limit of the function algebraically. (6 points)

limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.
0
-9
Does not exist
9
9. 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 six that ends at the open point 2, 6, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 2.

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. . (7 points)

-2; 6
1; 1
Does not exist; does not exist
6; -2
10. Use the given graph to determine the limit, if it exists.

A coordinate graph is shown with a downward sloped line crossing the y axis at the origin that ends at the open point 3, negative 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, negative 4.

Find limit as x approaches three from the right of f of x. . (7 points)

-1
7
-4
Does not exist
11. Find the indicated limit, if it exists. (7 points)

limit of f of x as x approaches negative 4 where f of x equals x plus 3 when x is less than negative 4 and f of x equals 3 minus x when x is greater than or equal to negative 4
The limit does not exist.
-1
-4
7
12. Find the indicated limit, if it exists. (7 points)

limit of f of x as x approaches 0 where f of x equals 9 minus x squared when x is less than 0, 9 when x equals 0, and negative 4 x plus 9 when x is greater than 0
The limit does not exist.
9
-4
-13
13. 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 . (7 points)
-∞; x = 7
∞; x = -7
-∞; x = -7
1 ; no vertical asymptotes

Short Answers: 14. The position of an object at time t is given by s(t) = -9 – 3t. Find the instantaneous velocity at t = 8 by finding the derivative.

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

 
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