Consider the function $f(x) = \ln(x^2 + 1). $</p><p>a) Use integration by parts to find the indefinite integral of$f(x)$.

The diagram shows an eyepiece graticule and cell viewed through a microscope. When the eyepiece graticule was calibrated at this magnification, the whole length of the graticule shown covered 12 divisions of a stage micrometer scale.

There were 100 divisions in 10 mm of the stage micrometer.

What is the actual length of the cell?

A 2.5 um

В 3.6 um

С 360 um

D 3mm

The photomicrograph shows the ultrastructure of part of a cell.

Which statement about the type of cell shown in the photomicrograph is correct?

A It is a plant cell because it has both chloroplasts and a nucleus.

B It is a plant cell because it has chloroplasts.

C It is an animal cell because it has a cell membrane.

D It is an animal cell because it has mitochondria.

A student examined a slide of human blood with a light microscope and made a careful drawing of the different cell types. The student used an eyepiece graticule so that the relative sizes of the different cell types were drawn accurately.

In the drawing:

• red blood cells were 7 mm in diameter

• lymphocytes were 6 mm in diameter

• neutrophils were 14 mm in diameter.

What is the linear magnification of the drawing?

A. x10

B. x40

C. x100

D. x1000

The diagram shows a graduated slide, with divisions of 0.1 mm viewed using an eyepiece graticule.

Pollen grains were grown in a sugar solution and viewed using the eyepiece graticule. Diagram 1 shows the pollen grains at the start. Diagram 2 shows the pollen grains after four hours.

What is the growth rate of the pollen tubes?

A. 5 μmh^-1

B. 10 μmh-¹

C. 5 mmh^-1

D. 10 mmh^-1

What is the definition of the resolution of a light microscope?

A. the degree of sharpness produced by the microscope

B. the greatest distance between two objects visible in the same field of view

C. the minimum distance that allows two objects to be viewed as separate

D. the size of the smallest object visible using the microscope

The electron micrograph shows a type of virus at a magnification of x30 000.

What is the length of the virus?

A. 2.2x10³nm

B. 2.2x10²nm

C. 2.2x10¹nm

D. 2.2x10⁰nm

A student was given a photomicrograph of a cell and told the magnification of the image. The student was asked to calculate the actual size of the cell. Which row in the table explains how to do this?

Which row shows the correct order of size of these cell structures?

1 width of a mitochondrion

2 width of a ribosome

3 width of a cell surface membrane

4 width of a chloroplast

The diagram shows a stage micrometer scale viewed through an eyepiece containing a graticule.

The small divisions of the stage micrometer scale are 0.1 mm

The stage micrometer scale is replaced by a slide of a plant cell.

What is the actual length of the nucleus in the plant cell?

A. 8 μm

B. 25 μm

C. 200 μm

D. 0.8 mm