Download PTU B.Tech 2020 March CSE-IT 1st Sem MA 1130 Enriched Calculus I Question Paper

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Roll No. [ ] [ ] [ ] Total No. of Pages : 03

Total No. of Questions : 09

B.Tech. (Software Engineering) (Sem.-1)

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INSTRUCTIONS TO CANDIDATES :

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1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.


2. SECTION -B & C have FOUR questions each. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.



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3. Select atleast TWO questions from SECTION - B & C.

SECTION-A

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1. Attempt the following :
   
   
   
   1. Explain how the vertical line test is used to detect functions.
   
   
   2. Graph the parabola f (x) = x². Explain why the secant lines between the points (-a, f(-a)) and (a, f(a)) have zero slope.

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   3. Evaluate lim _x?a (x-a)/(vx - va), a > 0.
   
   
   4. Suppose h(x) = { 3x+b, x<2; x-2, x=2 }. Determine a value of the constant b for which lim _x?2 h(x) exists and state the value of the limit, if possible.
   
   

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   5. Discuss the continuity of f(x) = { xsin(1/x), x?0; 0, x=0 } at x=0.
   
   
   6. Use the definition of the derivative to determine d/dx(vx). Also find the equation of the line tangent to the graph vx at (4, 2).
   
   
   7. Compute the derivative of (x²+2x-110)e^5x.

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   8. Find dy/dx, when sin(xy) = x² + y.
   
   
   9. State second derivative test for local extrema.
   
   

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   10. Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width and height not exceeding 64 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?
   
   
   
   



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SECTION-B

2. 
   
   
   

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   1. Find the inverse of the function f(x) = x² + 4 and write it in the form y = f^-1(x). Also verify the relationships f(f^-1(x)) = x and f^-1(f(x))=x.
   
   
   2. Find the domain and range of the function f(x) = v(2+x).
   
   
   
   

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3. 
   
   
   
   1. Let f(x) = { -2x+4 if x<1; x=1 if x=1 }. Find the values of lim _x?1- f(x), lim _x?1+ f(x), and lim _x?1 f(x), or state that they do not exist.

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   2. Evaluate lim _x?0 (v(5+x) - v5)/x.
   
   
   
   

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4. 
   
   
   
   1. A particle moves along the curve 6y = x³ + 2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.
   
   

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   2. Prove that the function f(x)={ sin(x)/x if x<0; x+1 if x=0 } is everywhere continuous.
   
   
   
   



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5. 
   
   
   
   1. Find the derivative of (sinx+cosx)/(sinx-cosx).
   
   
   2. Find the maximum value of 2x³ - 24x + 107 in the interval [1, 3].

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SECTION-C

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6. 
   
   
   
   1. If f(x)=(x³-3x-1)/(x²+7), find f'(3).

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   2. A swimming pool is 50m long and 20m wide. Its depth decreases linearly along the length from 3m to 1m. It is initially empty and is filled at the rate of 1m³/minute. How fast is the water level rising 250 minutes after the filling begins? How long will it take to fill the pool?
   
   
   
   

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7. An 8-foot-tall fence runs parallel to the side of a house 3 feet away. What is the length of the shortest ladder that clears the fence and reaches the house? Assume that the vertical wall of the house and the horizontal ground have infinite extent.


8. 
   
   
   

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   1. Find the anti derivative of the function 4/x². Check your answer by taking derivative.
   
   
   2. If lim _x?0 (sin(2x)+asin(x))/x³ be finite, find the value of a and the limit.
   
   
   
   

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9. Use the graphing guidelines to graph the function f(x) = 10x²/(x²-1).

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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