Questions with Complete Solutions - Hamro CSIT

Show that y = x – 1/x is a solution of the differential equation xy’ + y = 2x.

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Find y’ if x³ + y³ = 6xy.

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Find where the function f(x) = 3×4 – 4×3 – 12 x2 + 5 is increasing and where it is decreasing.

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Find the Maclaurin series expansion of f(x) = e^x at x =0.

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Integrate ₀∫¹ x²√(x³ + 1) dx.

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(c) What is the temperature at a height of 2.5 km?

Not Answered First Semester Asked on 2080 Exam

(b) Draw a graph of the function in part(a). What does the slope represent?

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As dry air moves upward, it expands and cools. If the ground temperature is 20°C and the temperature at height of 1 km is 10C, express the temeperature T(in °C) as a function of height h(in kilometer), assuming that the linear model is appropriate.

Not Answered First Semester Asked on 2080 Exam

(b) Find the solution of the equation y²dy = x²dx that satisfies the initial condition y(0) = 2.

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(a)The area of the parabola y = x2 from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulitng surface.

Not Answered First Semester Asked on 2080 Exam

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