NU_CALCULUS II COMPETITION

The effect of the limit process on the Riemann Sum (with regard to the area A, under a curve y = f(x) over [a,b] ) includes the following except:

•  $\Delta x_k\ \rightarrow\ 0$  

•  $\sum_{k=1}^n\rightarrow\ \int_a^b$  

•  $f\left(x_k^{\cdot}\right)\ \rightarrow\ f\left(x\right)$  

•  $\Delta x_k\ \rightarrow\ dx$  

A solid of revolution is a . . . that is generated by revolving a . . . region about the axis of revolution.

• Plane, Solid

• Mass, Object

• Solid, Plane

• Solid, Shape

Choose one of the options. The general equation of a conic section is written as:
 $Ax^2$   +  $Bxy$   +   $Cy^2$   +  $Dx$   +  $Ey$   +  $F$     $\ge$  0

• False

• Not always

• True

A pair of intersecting lines is an example of a degenerate conic section

• False

• Not always

• True

Which of the following conic sections is associated with asymptotes?

• Parabola

• Circle

• Ellipse

• Hyperbola

Work is done by applying a constant force W, on a body c, causing it to move from point a to point b on a flat surface. If b > a on the positive x-axis, the magnitude of this work done is given by:

• W * b

• W * c

• (b - a) * W

• a * W

A homogeneous lamina has non-uniform composition.

• False

• True

• Not always

This object in the image can be approximated to a lamina.

• True

• Iff it weighs below 5kg

• False

• Not always

The method of integrating $\int_{ }^{ }f\left(x\right)g\left(x\right)\ dx$  as described in the image is called . . .

• Variable integration

• Tabular method

• Integration by parts

• Reduction formula

For a given differential equation: $-4\frac{\text{d}^2x}{\text{d}y^2}\ +5\frac{\text{d}x}{\text{d}y}\ +8x\ +4\ =0$ . The order of the differential equation is:

• -4

• 5

• 2

• 8