Numerade

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Let $f(x) = \frac{6x \sin(8x) + px^2}{24 - 24 \cos(5x) - 300x^2}$. (a) Find the one and only value of the constant $p$ for which $\lim_{x \to 0} f(x)$ exists. Answer: $p =$ (b) Using the value of $p$ found in part (a), evaluate the limit. Answer: $\lim_{x \to 0} f(x) =$

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Long-term use of methamphetamine can result in which of the following A. Depression and suicide B. Hyper-tension C. Diarrhea D. Shingles

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A new element has been discovered. Its name is Hamiltonium (Hm), in honor of the chemist who first isolated it in the laboratory. As an ion, it has a charge of –2, and the oxyanion, HmO₃²⁻, is called hamiltonate. What is the name of the acid, H₂HmO₂?

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3. Let G be a group, and suppose that $x$ and $y$ are elements of G, each with finite order. Suppose $x$ and $y$ commute and that $(x) \cap (y) = \{e\}$. Let $g := xy$. Prove that $|g| = LCM(|x|, |y|)$.

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Sexual dimorphism is very common among pigs (and other species in the family Suidae). True False

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Which of the following statements about biological membrane structure is true? Fatty acids easily flip from one side to the other side of the membrane's lipid bilayer. The lipids that constitute the lipid bilayer are exclusively phospholipids. Unsaturated fatty acids pack closely together to form ordered arrays of lipids. The types of lipids in a lipid bilayer are distributed asymmetrically between the inner and outer monolayers of the bilayer in most membranes. Carbohydrates attached to membrane lipids are usually found on the cytosolic side of the membrane.

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Neuroticism is characterized by a person’s tendency to experience unpleasant emotions such as anger, anxiety, depression, and feelings of vulnerability. Question 3 Select one: True False

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Use the given information about the data set and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 20, range = 106, 8 classes The class width is (Type a whole number.)

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You roll a uniform cylinder and a uniform sphere from rest at the top of an inclined plane. If the condition of rolling without slipping is met, then what is the ratio of their acceleration? i.e. 5 16 0.10 9 0.14 15 0.07 10

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With the aid of a diagram explain on oligopolistic kinked demand curve. (10 Marks)

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andres h.