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University of Barishal

Department of Computer Science and Engineering

2nd Mid Exam

Course Title: Differential Calculus and Co-ordinate Geometry (MATH-1109)

Semester: 1st | Session: 24-25

Time: 100 minutes | Marks: 20.00

View 31 Topic-wise Questions for this Course

Figures in the right margin indicate marks.
Answer all the questions.

1.

a)

Show that the function

is continuous at the point x = 1 but f'(1) does not exist.

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3 Marks
b)

Find dy/dx (any two) if:

(i) x = at2, y = 2at,   (ii) y = (sinx) cosx  and (iii) y = tan-1 (sec x + tan x)

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2 Marks
c)

If the tangent to the curve √x + √y = √a at any point on it cuts the two axes at P and Q, show that OP + OQ = a, O being the origin.

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2 Marks
2.

a)

Find the volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius a. 

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2 Marks
b)

If y = cos(m sin-1 x) then prove that (1 - x²)yn+2 - (2n + 1)xyn+1 + (m² - n²)yn = 0.

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2 Marks
c)

Find the intervals on which the function f(x) = 2x³-3x² - 36x + 7 is increasing or decreasing. Also find the maxima and minima of f(x).

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3 Marks
3.

a)

Find the first four terms in the expansion of ln sin(x + h) in ascending powers of h. Hence find the value of ln sin 31° to four places of decimals, given ln 2 = 0.69315.

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2 Marks
b)

If, 

be finite, find the value of a and also the limit.

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2 Marks
c)

Find the equation of circle of curvature of the curve y = sinx at the point (π/2, 1).

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2 Marks
View 31 Topic-wise Questions for this Course

Contributors of this Question:

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Uploaded By: Mst.Nusrat Jahan Dec. 15, 2025, 6:37 p.m.
Converted By (Img/PDF to Text): Baishakhi Bir Dec. 29, 2025, 10:30 p.m.
Reviewed By: Obaydul Hasan Nayeem Dec. 30, 2025, 11:36 a.m.
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