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