2. Consider a function f(x) = cos a² + (5)². %3D (1) Show that f is continuous on R. (2) se the fact from part (1) to compute the limit lim cos V +()?. n-00

Q: Express the limit as a definite integral on the given interval. im. (4(x;") - 3x;JAx, [2, 7] i = 1 7…

A: By limit definition of a definite integral, limn→∞∑i=1nfxi*∆x=∫ab f(x)dx  where ∆x=b-an and…

Q: (th)-tsC by recognizing Evaluate the limit tan it as a derivative of Some function and using…

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Q: Is the function (x² - 1)/(x - 1) continuous at x = 1? Answer this question by evaluating f(1) and…

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Q: Use the squeeze theorem to evaluate lim tan(a) sin (z,M)-(0,0) |æ| + \y|\,

A: Since you have posted multiple questions, we will solve only first question for you. To get…

Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

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Q: 4. List the discontinuities for the function f(x) = cot(* :).

A: First write the given function into Numerator and denominator form and , to find the discontinuity…

Q: 1. Sketch the graph of a function f with the following properties. f'(x) > 0, for x 0 ƒ" (x) > 0,…

A: Sketch the graph of a function f with the following properties,

Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

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Q: 1 S(t – 4t) dt

A: Given that: The limit is limN→∞ ∑i =1N  iN2 - 4iN×iN .

Q: 1. Graph the following functions on the same set of axes on the interval [-7, 57/2). f(t) = 2 cos t…

A: % Matlab code% specifying range of tt=[-pi:0.1:(5*pi/2)];% defining functions f(t) and g(t)f=…

Q: 1. Use the limit formula, and showing all work, find f'(x) for f(x) = -3x³ + 2x -1.

A: To find the differentiation of given function.

Q: The limit represents the derivative of some function f at some number a. State such an f and a. lim…

A: Given that : The limit represent the derivative of some function f at some number a . limh→0 cos π+h…

Q: Consider the function f(x) = x3 – 2x2 - 14x + 13. (a) Use a graphing calculator to graph fin an…

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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.