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Calc 1 5.1

 

<== Calculus 1
Number Question Answer
See the work
1. (A) Estimate the area under the graph of

f(x) = 25 - x^2

from x = 0 to x = 5 using 5 approximating rectangles and right endpoints.

Estimate =

(B) Repeat part (A) using left endpoints.

Estimate =
(C) Repeat part (A) using midpoints.

Estimate =
A) 70

B) 95

C) 83.75
The work

Point Cost: 3
2. Speedometer readings for a motorcycle at 12-seconds intervals are given in the table.
t(s)01224364860
v (ft/s)252730243025

(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.


(b) Give another estimate using the velocities at the end of the time periods.
A) 1632

B) 1632

The work

Point Cost: 1
3. Estimate the area under the graph of

f(x) = 2 x^3 + 3
from x = -1 to x = 3, first using 4 approximating rectangles and right endpoints, and then improving your estimate using 8 approximating rectangles and right endpoints.

4 Rectangles =

8 Rectangles =

(B) Repeat part (A) using left endpoints.

4 Rectangles =

8 Rectangles =

(C) Repeat part (A) using midpoints.

4 Rectangles =

8 Rectangles =
A) 4 Rectangles = 84
    8 Rectangles = 67

B) 4 Rectangles = 28
    8 Rectangles = 39

C) 4 Rectangles = 50
    8 Rectangles = 51.5

The work

Point Cost: 3
4. The value of the limit

\lim_{n
ightarrow\infty}\sum_{i=1}^{n} rac{4}{n}
    \sqrt{6 + rac{4 i}{n}}
is equal to the area below the graph of a function f (x) on an interval [A,B]. Find f, A, and B.

f (x) =

A = (use A=0)

B =
f (x) =

A = 0

B = 4
The work

Point Cost: 1
5. The value of the limit

\lim_{n
ightarrow\infty}\sum_{i=1}^{n} rac{\pi}{4 n}
    	an\left(rac{i \pi}{8 n}
ight)
is equal to the area below the graph of a function f (x) on an interval [A,B]. Find f, A, and B.

f (x) =

A =

B =
f (x) = tan(x/2)

A = 0

B = 0.785
The work

Point Cost: 1
6. Estimate the area under the graph of

f (x) = 4/x
from x = 1 to x = 6 using 5 approximating rectangles and right endpoints.

Estimate =

(B) Repeat part (A) using left endpoints.

Estimate =
A) 5.8

B) 137/15
The work

Point Cost: 3