In this calculus article, we will talk about the methods for actually solving or evaluating limits. There are practice questions included, labeled PRACTICE, and they are there for you to test your understanding of the different methods. The answers are at the very bottom. Enjoy!
Learn about two very cool theorems in calculus using limits and graphing! The squeeze theorem is a useful tool for analyzing the limit of a function at a certain point, often when other methods (such as factoring or multiplying by the conjugate) do not work. This theorem also has other names like the Sandwich Theorem or the Pinch Theorem, but it is most commonly called the Squeeze Theorem. The Intermediate Value Theorem, often abbreviated as IVT, deals with a single function unlike the Squeeze Theorem.
Whether it’s a violin or a harmonica, learning to play an instrument takes time and effort to “perfect.” Musicians put hours and hours of hard work to perform in concerts, participate in competitions, or even just practice for fun at home. It can be frustrating to play the same piece hundreds and hundreds of times, especially if you still can’t get one section down. However, all of these hours of practicing actually do more than just putting on a perfect performance or impressing your family; playing an instrument can help your physical and mental state.
Rheumatoid arthritis is an autoimmune disease characterized by chronic inflammation in the joints of hands, feet, knees, etc. In this quick and easy lesson, we explain the standard medical treatment for patients with rheumatoid arthritis at the USMLE immunology level, including DMARDS (synthetics and biologics), NSAIDS, and glucocorticoids.
There are two types of chemoreceptors that help control and regulate our respiratory rate: 1) central chemoreceptors and 2) peripheral chemoreceptors. Both central chemoreceptors and peripheral chemoreceptors send signals to the main respiratory center in the brain that unconsciously tells our bodies to increase or reduce pulmonary ventilation. In this lesson, we describe the differences and similarities of central chemoreceptors and peripheral chemoreceptors for the pulmonary system.
Native to New Guinea, bananas prefer tropical climates and can be grown year round. In terms of produce, the biggest distinction is between bananas and plantains, both of which belong to the same genus (Musa) and come in a range of cultivars, or varieties. Bananas are generally eaten raw or as part of a dessert or baked good. Plantains are a staple crop, culinary distinct due to their higher starch content, predisposing them to being cooked and fried as part of meals or snacks.
Biology Unit 5 Study Guide: Evolution. After his visit to the Galapagos Islands, Darwin came up with the theory of evolution. This theory stated that organisms change over time. The way that organisms change is through the process of natural selection. With examples, practice questions, and answers to help make evolution respiration easy to learn!
Biology Unit 4 Study Guide: Genetics, Meiosis, DNA and Protein Synthesis. With examples and answers to help make meiosis, DNA replication, and RNA translation easy to learn!
To answer this question we will first have to review the physical properties of light and go over the basics of optics, which is the study of the relationship between sight and light. Visible light is a section of the electromagnetic spectrum, and it is the only portion that people can see. While electromagnetic radiation can be measured via its various prosperities, such as frequency or energy, it is most commonly categorized by wavelength. Taking one step back, radiation is the transfer of energy in the form of waves or particles. For electromagnetic radiation, wavelength is determined by measuring photons. Put simply, photons are massless particles that also exhibit the characteristics of waves. To measure wavelength a point is designated on one wave (usually a peak or trough) and the length between it and that same point on the next wave gives you the wavelength.
Hi Everyone! My friend just published a biology study guide book and it’s currently on sale! This book on biology study guides contains practice review questions and answers. Study Guides: Biology Unit Review Practice Questions and Answers . This interactive study guide of worksheets contains questions and answers to help you understand biology. Each unit contains information on key topics to review to further your understanding of biology. The units covered in this book include: ecology, biomolecules and cell biology, energy, photosynthesis, cellular respiration, cell division, mitosis, meiosis, protein synthesis, genetics, and evolution. Award-winning author and teacher Dr. Sam J. Alex created this study guide while inspired by students and teachers. All proceeds donated! Hope you find this book helpful on your journey into the wonderful world of biology and beyond!
Biology Unit 3 Study Guide: Cellular Processes – Photosynthesis and Cellular Respiration. Light Reactions and Calvin Cycle. Glycolysis, Krebs Cycle, and Electron Transport Chain. With examples and answers to help make photosynthesis and cellular respiration easy to learn!
In this quick, easy-to-understand lesson, we learn about secondary hypertension for USMLE and medicine. Secondary hypertension is defined as high blood pressure (>140/90 or >130/80) caused by an underlying disease, medical condition, or drugs. While primary essential hypertension comprises of the majority of hypertension cases (90%), only 10% of patient cases is secondary hypertension.
Direct vs Indirect Hernia: What is the difference between direct and indirect inguinal hernias? In this easy-to-understand lesson, we explore the differences between direct inguinal hernias and indirect inguinal hernias. Overall, an inguinal hernia is a medical condition, where protrusion or bulge of abdominal contents into the groin area and/or inguinal canal. There are two types of inguinal hernias: 1) direct inguinal hernia and 2) indirect inguinal hernia.
When you hear the word “robot”, what image usually comes to mind? Is it a metallic, boxy machine? A sleek android that talks to people? A robot is a machine that is automatically operated and completes tasks in replacement for humans. Some robots are humanoid and have actions that resemble human movement, such as ASIMO (Advanced Step in Innovative Mobility), a robot created by Honda that can walk with two legs (Honda).
Microfilaments and microtubules are both important elements of the cytoskeleton, maintaining the structure and integrity of the cell, but there are several differences between microfilaments and microtubules. In this article, we share this information on microfilaments versus microtubules.
Microfilament and Microtubulues are made from different individual subunits. Microfilaments are made from ACTIN, while microtubules are made from TUBULIN.
Making up around 75% of all animal species in the world, arthropods are are a vast phylum of the kingdom Animalia. The name comes from the Greek words “arthro”, meaning joint, and “podos”, meaning legs. While they all share segmented bodies with joined legs, members in this phylum vary wildly, from butterflies and millipedes, to scorpions and lobsters. They are also all invertebrates, which means that they do not have backbones. Instead, they use hard exoskeletons to protect themselves, which are made out of chitin. Because these exoskeletons are relatively inflexible, arthropods molt as they grow larger, which means they shed their exoskeletons.
You probably go to sleep most – if not all – nights. You probably have dreamt during many of these nights. And you might feel rested every time you go to sleep. Yet did you know about the complex mental processes that happen every time we go to sleep?
What is the difference between Kwashiorkor and Marasmus? USMLE protein-energy malnutrition diseases; we explain the differences, including causes, symptoms, comparative medical charts.
The novel COVID-19 is leaving astonishing traces of deaths and illnesses as it rapidly encroaches upon our everyday lives. Schools are closed. Unemployment is surging. People experience dreadful losses of their family and friends. Luckily, however, the exponential curve of COVID-19 seems to have flattened within the past few weeks for many of the countries, and some even seem to have downward-sloping trends. So, should we feel relieved and expect the curve to hit 0 soon?
Phosphorus Part 2: Health Risks and Disadvantages. Part 1 of this article described the uses and advantages of the element phosphorus. However, there are also various health risks that come with using phosphorus in our lives.
How did flightless birds evolve? How did the evolution of the shrinking cod come to be? In this lesson, we learn about the evolution of the flightless birds, such as cormorants, and the evolution of the shrinking cod in our biology selection case studies.
Biology Unit 2 Study Guide: Basic Building Blocks of Life. Protein, lipid, nucleic acid, carbohydrate, properties of water, enzymes, organelles. With examples and answers to help make biomolecules easy to learn!
Biology Unit 1 Study Guide: Ecology and Scientific Method, including Characteristics of Life, Biodiversity, Cycles of Matter, and Global Change. With examples and answers to help make ecology easy to learn!
In this lesson, we explain the differences between flippase, floppase, and scramblase. Flippase vs Floppase vs Scramblase as lipid transporters in the cell membrane with Quick and Easy Explanation
In this lesson, we explain what types of molecules can pass through the cell plasma membrane and what are the factors that determine whether a molecule can cross a cell membrane: Quick and Easy Explanation on the Cell Membrane