Mathematics I TU Board 2075 question paper

A function is defined by f(x) = |x| , calculate f(-3), f(4), and sketch the graph.

Find the domain and sketch the graph of the function $f(x)=x^2–6x$.

Find the Maclaurin series for cos x and prove that it represents cos x for all x.

If f(x, y) = $\frac{y}{x}$ does ${\lim }_{(x,y)\to (0,0)}f(x,y)$ exists? Justify

Prove that the ${\lim }_{x\to 2}\frac{|x–2|}{x–2}$ doesn't exist.

Estimate the area between the curve y = x^2 and the lines y = 1 and y = 2.

Find the volume of a sphere of radius r

Calculate ${\int }_R\int f(x,y)dA$ for f(x,y) = 100 – 6x^2y and $R:0\le x\le 2,-1\le y\le 1$

If f(x) = $\sqrt{2-x}$ and g(x) = $\sqrt{x}$, Find fog and fof

Define continuity on an interval. Show that the function $f(x)=1–\sqrt{1-x^2}$ on the continuous on the interval [1,-1].

Verify Mean value theorem of f(x) = x^3 – 3x + 2 for [-1, 2].

Stating with x_1 = 2, find the third approximation x_3 to the root of the equation x^3 – 2x – 5 = 0

Evaluate ${\int }_0^{\infty }{x}^3\sqrt{1–x^4}$ dx

Find the volume of the resulting solid which is enclosed by the curve y = x and y = x^2 is rotated about the x-axis.

Find the solution of y" + 4y' + 4 = 0.

Determine whether the series ${\sum }_{n=1}^{\infty }\frac{n^2}{5n^2+4}$ converges or diverges.

Find $\frac{\partial z}{\partial x}and\frac{\partial z}{\partial y}$ if z is defined as a function of x and y by the equation $x^3+y^3+z^3+6xyz=1$.

Find the extreme values of the function $f(x,y)=x^2+2y^2$ on the circle $x^2+y^2=1$.