StudyNp | BIT First Semester – 2081 Question | Basic Mathematics (Syllabus Wise)

Bachelors Level/First Year/First Semester/Science bit/first semester/basic mathematics/syllabus wise questions

Institute of Science and Technology, TU

Basic Mathematics (MTH104)

Year Asked: 2081, syllabus wise question

Find the volume of the solid obtained by rotating about the y-axis the region bounded by

y = x

and

y = x^2

. [5]

Verify mean value theorem for the function

f(x) = x^2 + 3x + 1

[-1,1]

. [5]

Find the derivative of

y = \dfrac{\tan^{-1} x}{\sqrt{x}}

with respect to

x

. Find the area of the region bounded by

y = -x

and

x = y^2 + 3y

. [5+5]

Use Newton's method to find

\sqrt[4]{10}

correct to four decimal places. [5]

What is initial value problem? Find the solution of the initial value problem

x \dfrac{dy}{dx} - y = x^2

y(2) = 5

. Evaluate:

\lim_{x \to \infty} \dfrac{3x^2 - 5x + 2}{5x^2 + 8x + 7}

. [1+4+5]

Test whether the series

\sum_{n=2}^{\infty} \dfrac{2}{n^2 - 1}

converges or diverges. [5]

Explain the meaning

\lim_{x \to 2} f(x) = 5

. Is it possible for this statement to be true, yet

f(2) = 3

? Explain. Draw a graph of the function

f(x) = x^2 + 4

and find its domain and range. [5+5]

Test whether the function

f(x) = \begin{cases} \dfrac{x^2 - 2x}{x - 2}, & x \ne 2 \\ 1, & x = 2 \end{cases}

is continuous or discontinuous at

x = 2

. Explain. [5]

Find the partial derivatives

f_x

f_y

and

f_{xy}

f(x,y) = \sqrt{x} y^3 + x^4 y

(-4,1)

. [5]

Evaluate:

\int \sqrt{4 - x^2} \, dx

. [5]

Evaluate:

\int_0^5 \dfrac{dx}{\sqrt{x - 2}}

, if it exists. [5]

Evaluate:

\int_0^{\pi} x \sin x \, dx

. [5]