Mathematics I
This course makes students able to understand and formulate real-world problems into mathematical statements and also develop solutions to mathematical problems at the level appropriate to the course.
Tribhuvan University
Institute of Science and Technology
2081
Bachelor Level / first-semester / Science
Computer Science and Information Technology( MTH117 )
Mathematics I
Full Marks: 80 + 20
Pass Marks: 32 + 8
Time: 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.
Section A
Attempt any TWO questions:
Sketch the graph of f(x)=x2 . Find its domain and range.
Estimate the value of limx→0 ( (√(x2 + 9) ) – 3 )/ x2
Where is the function f(x)=∣x∣ differentiable? Discuss.
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?
Find the solution of the initial value problem: x2y′+ xy = 1, y(1) = 2, x>0.
Find the area enclosed by the line y=x−1 and the parabola y 2=2x+6
Section B
Attempt any EIGHT questions:
Evaluate:
Find the Maclaurin series expansion of f ( x ) = sin x for all x.
Find the unit normal and binormal vectors for the circular helix:
Determine whether the sequence an = (-1)n is convergent or divergent.
The position vector of an object moving in a plane is given by
Find its velocity, speed, and acceleration when and illustrate geometrically.
Show that every member of the family of functions:
is a solution of the differential equation:
Use cylindrical shells to find the volume of the solid obtained by rotating about the -axis the region under the curve from 0 to 1.