Related Concept Videos

Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
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Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
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Golgi Apparatus01:49

Golgi Apparatus

As they leave the Endoplasmic Reticulum (ER), properly folded and assembled proteins are selectively packaged into vesicles. These vesicles are transported by microtubule-based motor proteins and fuse together to form vesicular tubular clusters, subsequently arriving at the Golgi apparatus, a eukaryotic endomembrane organelle that often has a distinctive ribbon-like appearance.
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Two-dimensional Gel Electrophoresis01:22

Two-dimensional Gel Electrophoresis

Two-dimensional gel electrophoresis is a high-resolution protein separation method first introduced by O' Farrell and Klose in 1975. This method involves protein separation by two dimensions, mass and charge, making it more accurate than one-dimensional gel electrophoresis.
The first dimension separation uses the isoelectric focusing or IEF technique performed on immobilized pH gradient (IPG) strips that separate proteins according to their isoelectric points.
Biological samples, such...
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DNA Agarose Gel Electrophoresis02:35

DNA Agarose Gel Electrophoresis

Agarose gel electrophoresis is a laboratory technique commonly used to separate DNA fragments by size. However, it can also be used to isolate and purify DNA fragments using a gel extraction protocol.
Gel extraction follows five major steps: running gel electrophoresis to separate fragments, isolating the individual bands, extracting DNA from those bands, and removing the dye and salts from the extracted mixture to obtain pure DNA.
In cloning experiments, both the insert and vector DNA...
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Golgi Apparatus01:09

Golgi Apparatus

Properly folded and assembled proteins are selectively packaged into vesicles that exit the ER. Motor proteins transport these vesicles to the Golgi apparatus for adding modifications that make these proteins functional at their destination.
The Golgi apparatus is a eukaryotic organelle that has a distinctive ribbon-like appearance. It is a primary sorting and dispatch station for cargo arriving from the ER. Newly arriving vesicles enter the cis face of the Golgi, closest to the ER, and are...
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