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2 AY:2019-2020 Sem-2 MATH/200 . Calculus Additional Instructions: 1. Students are advised to answer all the...

Question:

2 AY:2019-2020 Sem-2 MATH/200 . Calculus Additional Instructions: 1. Students are advised to answer all the assignment questi

() To what new value should f (2) be assigned to make the function continuous atx=27 (Each part / Mark) 1. (b) Evaluate: lim

2 AY:2019-2020 Sem-2 MATH/200 . Calculus Additional Instructions: 1. Students are advised to answer all the assignment questions clearly in A4 sheets with proper question numbers and all required steps. 2. Write the question number, page number and ID in all the pages of your answer sheet. 3. Your answers will be marked based on completeness of the requirements and clarity. 4. Use only blue or black pen for answers/drawing. 5. Submit your assignment as a pdf only through the e learning on or before the assignment deadline. Answer all the questions. Each question carries 10 Marks. (5 x 10 = 50 Marks 1. (a) Refer to the graph and answer the following questions (5 Marks) m) Find lim (*) y = f(x) () Find lim (*) 2 1 3 5 (ii) Find lim : (*) (iv) Is the functionſ continuous at the point x =4? If not continuous, give a reason. (1) To what new value should f (2) be assigned to make the function continuous atx=2? (Each part / Mark) 1. (b) Evaluate: lim (x-1)(12? +3-2) Vx+8 - 3 (5 Marks) 3 AY:2019-2020 Sew-2 MATHI200 - Calculus ! 2. (a) s = 88 -25+ + 3 represents the position of a body moving in a line with sin meters and t in seconds with OSIS3 (5 Marks) a) Find the body's displacement for the given interval. b) Find the body's speed and acceleration at the end points of the interval. c) Find the body's acceleration when the velocity is zero. d) Find the body's speed when the acceleration is zero.
() To what new value should f (2) be assigned to make the function continuous atx=27 (Each part / Mark) 1. (b) Evaluate: lim (x-1)(1.7+3-2) Vx+8-3 (5 Marks) 3 AY:2019-2020 Sem-2 MATH/200 - Calculus / 2. (a) s = 84-254 +3 represents the position of a body moving in a line with sin meters and t in seconds with OSIS3 (5 Marks) a) Find the body's displacement for the given interval. b) Find the body's speed and acceleration at the end points of the interval. c) Find the body's acceleration when the velocity is zero. d) Find the body's speed when the acceleration is zero. dy 2. (b) Find , for the function: y= Acos" (1 + /) + (sin x) + 2"* + xel+(2-7) (5 Marks) (Derivative of each term - / Mark) dy 3. (a) Find for the function: y = sin(x) cot (5 Marks) (Rule . Mark Applying the rule. 3 Marks Simplification Mark) dy 3. (b) Find de (5 Marks) for the following function. Write down the answer in the simplest form (x+2)(2x+1) (Rule. Mark Applying the rule 3 Marks Simplification Mark) 4. (a) Find the equation of the line tangent to the curve at the given point for the parametric equations. x1+cost. y - 1-sin/ at (5 Marks) 6 (Derivative - 3 Marks Equation of langen- 2 Marks) 4. (b) Verify Mean Value Theorem for the function /(x)=5x - 4x +5 on (0,2). (5 Marks) 5. (B) Use the definition to find the function's derivative and then evaluate the derivative at the indicated point. 2 (5 Marks) 2x+x (5 Marks) dt 5. b) Use implicit differentiation to find for the following function 5-*** -cos" (wy) - 2 sin(3x+y) (Differentiation - 3 Marks dy - 2 Marks) dx ************************************* RRRRRRRRRR ALL THE BEST EL

Answers

1) ) 9 나 , f(x) (7) = o. 키 (7) = 2. 제5 1) P(x)= 2.5 15 NO : 나 반 위 15년 it , fla)=f(u)=2 u → 저 •; tft) - IT - 3. we shoueth ass

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