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University of Barishal

Department of Computer Science and Engineering

Final Exam

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

Semester: 1st | Session: 23-24

Time: 180 minutes | Marks: 60.00

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Answer any five Questions from the followings.

1.

a) Evaluate the following limit.

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4 Marks
b) Evaluate the following limit.

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c) Evaluate the following limit.

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2.

a) Find the slopes of the tangent lines to the curve

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b) Find dy/dx for the followings

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6 Marks
3.

a) Show that Mean Value Theorem holds for

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b) Show that Rolle's Theorem holds for

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4.

a) Find the local extrema of

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b) Find Find the inflection points of f(x) and determine the concavity around them. d dy/dx for the followings

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5.

a) Compute the curvature for f(x) = x²-6x+15.

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b) Compute the radius and center of curvature for f(x) = x³-4x+15.

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6.

a) Find the angle between the lines 3x-4y +6 = 0 and 4y +6 = 0

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b) Find the distance of the point (-2,1) from the line 3x-4y +6=0.

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7.

a) Check orthogonality for the circles x²+y²+4x+6y+9=0 and x²+y²-6x-8y+15=0.

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b) Find the radical axis of the circles x² + y²+ 4x + 6y + 9 = 0 and x² + y² - 6x - 8y + 15=0.

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8.

a) Find the tangent to x²+y²=25 at point (3,4).

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b) Find the chord of contact from (7,2) to the circle x²+y²=9.

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View 31 Topic-wise Questions for this Course

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Uploaded By: Israt Jahan May 14, 2025, 2:22 p.m.
Converted By (Img/PDF to Text): Nahare Jannat Oct. 22, 2025, 10:52 p.m.
Reviewed By: Obaydul Hasan Nayeem Nov. 24, 2025, 11:04 a.m.
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