Math Assignment

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 ofthe assignment which is 50 marks Formative feedback on the complete assignment draft will be provided if the draft issubmitted at least 10 days before the final submission date. Feedback after final evaluation will be provided by 25/06/2020Module Learning OutcomesThe following LOs are achieved by the student by completing the assignment successfully1) Compute Limit and derivative of a function2) Able to apply derivatives in finding extreme valuesAssignment ObjectiveTo test the Knowledge and understanding of the student for the above mentioned LOAssignment Tasks:1. a. Evaluate the following limit:lim(2????3−128) ????→4 √????−2b. 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_01Page 1 of 78. Find.????????implicitly, if ???? (???? − 1) sin(2???? 5????) = ln(√7) −???? 2− cot(2????)MEC_AMO_TEM_034_01Page 2 of 7lim ????→07???? cos(????2)−7???? 5????2− lim [ ????→0sin(−2????)sin(5????)sin(7????) 2????3cos(????)]Engineering Mathematics-1 (MASC 0009.2) – Spring – 2020– CW (Assignment-1) – All – QP2. 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 only3. Find the derivative of ????(????) = ???????????? (5???? 7), by first principle of differentiation4. 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) = ????→22 ????,????≤02???? − 2, 0 < ???? ≤ 3????3 , 3<????<49, ????≥4 {7. Find the second derivative of the following function:???? = ????????2 ln(7????−???? 5????3) − 52???? 3???? √???? 3√???? ???????????????? 55Engineering Mathematics-1 (MASC 0009.2) – Spring – 2020–18/05/202025mathematics