Given that for each a E (0, 1) lim t "(1 – t)"dt exists. Let, this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1). The value of g is

Q: If lim (æ) – f(a) x - a | exists, then f is differentiable at a. Select one: True False

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Q: Let f(x) be a function of one variable defined near x = a. Given a number M, set

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Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

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Q: 15. Vlad and Karl discuss about the continuity of the given function. Vlad asserts that the function…

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Q: 8. Use the alternate form of the denivative: lim f(x)-flc) to show that f(x) = | x + al %3D X→し is…

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Q: Question: 1 a) Find and sketch the domain of the function f(x,y) = + Vx+1- log:(x² + y² – 4). b)…

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Q: State the Fundamental Theorem of Calculus (Part I and Part II). Hence or otherwise: (a) If u is a…

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Q: 5. Determine the infinite limit. a). f(x) = lim +1 x-5 2-t b). ƒ(t) = lim t→1 (t–1)2 x→5-

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Q: Find the d. c. of T from definition.

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Q: a. If f is continuous, then ſ f(x) dx = lim ſ´, f(x) dx. t-00 b. If f(x) < g(x) and g(x) dx…

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Q: 6. Prove that if f RR is continuous with limx→∞ f (x) limx→∞ f (x) f(c) > L for some c E R, then f…

A: The answer provided below has been developed in a clear step by step manner.

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Q: In a model of the nervous system, the intensity of excitation of a nerve pathway is given by I = E[1…

A: Given  that: I=E1-e-a(S-h)E

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Q: 4. Let function g: R → R be defined by g(x) = |x|. g(0+h)-g(0) h B. The value of lim 9(0+ h) − g(0)…

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Q: Prove that if S(c +h) – f(c) lim h exists, then f is continuous at c.

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Q: 1. Consider the function given by if r € QU [0, 1] f(x) = 1- I 1 ° if r E Q°U [0, 1] Determine if…

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Q: Let y=f(x).Which of the following correctly defines dx [fk+Ax)-fw] a. lim Ax+xL Ax Ob. lim Ax+x…

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Q: Show that if limn→∞ an = 0, then Θ(an + 1) = Θ(1).

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.