Page 13 - Module 1 in MATH 1 (Calculus)

PRACTICE EXERCISES:

Direction: Solve the following.

1. If ( ) = 2 , show that (a) ( + 3) − ( − 1) = 15 ( ) and (b) ( +3) = (4).
2 ( −1)
2
2. Let ( ) = − 2 + 3, evaluate (a) ( + ℎ), (b) ( +ℎ)− ( ) .
ℎ
3. A rectangular plot requires 2000 of fencing to enclose it. If one of its dimensions is (in
), express its area (in ) as a function of , and determine the domain of
the function.

Quiz # 1

Direction: Solve the following as indicated. Use separate sheets of paper for your solution. You
may also use graphing paper for your graphs.

1. If ( ) = − + , find (a) (0); (b) (3); (c) (−2).

2. If ( ) = − , show that ( + 1) = (− )

3. Draw the graphs of the following functions, and find their domains and ranges:

(a) ( ) = − + 1
− , 0 < < 1
(b) ( ) = {
, 1 ≥

4. Evaluate the expression ( +ℎ)− ( ) for the following functions :
ℎ
(a) ( ) = − ;

(b) ( ) = √

5. From each corner of a square of tin, 10 ℎ on a side, small squares of side (in
ℎ ) are removed, and the edges are turned up to form an open box. Express the
volume of the box (in ℎ ) as a function of , and determine the domain of the
function. Show a sketch of the figure.

Assignment # 1:

Direction: Give one real-world or situational example of a function and explain briefly. Make a
video record report of your output. You must limit the time of your video report to a minimum of 3
minutes and a maximum of 5 minutes. You may upload your report on our Google Classroom or
save it in your cellphone or laptop and submit it through Facebook messenger.

References/Reading Materials/ Open Educational Resource

1. Lial, Greenwell & Ritchey: Calculus with Applications: 8 Edition, Pearson Education South Asia
th
PTE LTD. 2006.
nd
2. Lax & Terrell: Calculus with Applications: 2 Edition, Springer. 2012 (eBook)
3. Ayres & Mendelson: Schaum’s Outline of Theory and Problems of Differential and Integral
Calculus: 3 Edition, McGraw-Hill Companies, Inc. 1990. (eBook)
rd
4. https://www.youtube.com/watch?v=Uz0MtFlLD-k&t=5s (Open Educational Resource)
5. http://www.studypug.com (Open Educational Resource)
6. phlconnect.ched.gov.ph (Open Educational Resource)

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