Precalculus homework help

Engineering Mathematics-1 Level: 1 Max. Marks: 100Instructions to Student:
 Answer all questions.
 Deadline of submission: 18/05/2020 (23:59)
 The marks received on the assignment will be scaled down to the actual weightage of
the assignment which is 50 marks
 Formative feedback on the complete assignment draft will be provided if the draft is
submitted at least 10 days before the final submission date.
 Feedback after final evaluation will be provided by 25/06/2020
Module Learning Outcomes
The following LOs are achieved by the student by completing the assignment successfully
1) Compute Limit and derivative of a function
2) Able to apply derivatives in finding extreme values
Assignment Objective
To test the Knowledge and understanding of the student for the above mentioned LO
Assignment Tasks:
1. a. Evaluate the following limit:
lim(2????3−128) ????→4 √????−2
b. Find the number ???? ????????????h ????h???????? lim (3????2+????????+????+3) exists, then find the limit ????→−2 ????2+????−2
(8 marks) (7 marks)
MEC_AMO_TEM_034_01
Page 1 of 7
8. Find
.
????????
implicitly, if ???? (???? − 1) + sin(2???? + 5????) = ln(√7) −
????+2
− cot(2????)
MEC_AMO_TEM_034_01
Page 2 of 7
lim ????→0
7???? cos(????2)−7???? 5????2
− lim [ ????→0
sin(−2????)sin(5????)sin(7????) 2????3cos(????)
]
Engineering Mathematics-1 (MASC 0009.2) – Spring – 2020– CW (Assignment-1) – All – QP
2. a. A particle moves in a straight line along with the ???? − ???????????????? its displacement is given by the equation ????(????) = 5????3 − 8????2 + 12???? + 6, ???? ≥ 0, where ???? is measured in seconds and s is measured in meters. Find:
i. The velocity function of the particle at time ????
ii. The acceleration function of the particle at time t. iii. The acceleration after 5 seconds
(2marks) (2marks) (1marks)
b. Find the derivative of ???? = 5????????????3(????) + ????????????2(3????2 − 4????) − csc(√2???? − 1 )and express your sin(3−2????)
answer in terms of sin and cos only
3. Find the derivative of ????(????) = ???????????? (5???? + 7), by first principle of differentiation
4. Find the points of local maxima and minima for the function ????(????) = ????4 − 18????2 − 9 5. a. For which value of n, does the lim −????????4+16???? = 2
(15marks) (10 marks)
(10 marks)
(5 marks)
(10 marks)
(5 marks)
(15 marks) (10 marks)
b. Evaluate the following limits:
????→2 32−????5
6. Evaluate lim ????(????), where f is defined by f(x) = ????→2
2 ????,????≤0
2???? − 2, 0 < ???? ≤ 3
????
3 , 3<????<4
9, ????≥4 {
7. Find the second derivative of the following function:
???? = ????????2 +ln(7????−???? + 5????3) − 52???? + 3???? √???? 3
√???? ???????????????? 5
5
Engineering Mathematics-1 (MASC 0009.2) – Spring – 2020–