Tribhuvan University
Bachelor of Science in Computer Science and Information Technology
Semester 1 · TU Board 2081
Course Title: Mathematics I (MTH117)
Full Marks: 80Pass Marks: 32Time: 3 hours
Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.
Group A
Attempt any TWO questions:(2 × 20 = 40)
- 1.20
Sketch the graph of f(x)=x^2 . Find its domain and range.
Answer comingAlso asked in 2080, 2075
- 2.20
Where is the function f(x)=∣x∣ differentiable? Discuss.
- 3.20
Find the solution of the initial value problem: x^2y′+ xy = 1, y(1) = 2, x>0.
Answer comingAlso asked in 2079, 2078, 2074
- •20
Estimate the value of lim_x→0 ( (√(x^2 + 9) ) – 3 )/ x^2
Answer comingAlso asked in 2080
- •20
A farmer has 1200 m of fencing and wants to fence off a rectangular field that borders a straight river. He does not need to fence along the river. What are the dimensions of the field that has the largest area?
View answerAlso asked in 2077
- •20
Find the area enclosed by the line y=x−1 and the parabola y ^2=2x+6
Group B
Attempt any EIGHT questions:(8 × 5 = 40)
- 4.5
Evaluate:
[figure in the original paper]
- 5.5
Find the Maclaurin series expansion of f ( x ) = sin x for all x.
Answer comingAlso asked in 2080, 2079, 2077, 2075, 2074
- 6.5
Find the unit normal and binormal vectors for the circular helix:
[figure in the original paper]
- 8.5
Determine whether the sequence a_n = (-1)^n is convergent or divergent.
- 9.5
The position vector of an object moving in a plane is given by
[figure in the original paper]
Find its velocity, speed, and acceleration when t=1 and illustrate geometrically.
- 10.5
Show that every member of the family of functions:
[figure in the original paper]
is a solution of the differential equation:
[figure in the original paper]
- 11.5
[figure in the original paper]
- 12.5
Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y= _/x from 0 to 1.
Answer comingAlso asked in 2078, 2077, 2075
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