Sketch the graph of f.  Then identify the values of c for which the limit f(x) exists as x-->c.          {sin x, x less than 0 f(x) = {1-cos x, 0 less than or = to x less than or = to Pi          {cos x, x greater than Pi

Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Graph ƒ(x) = tan-1 x + tan-1(1/x) for -5<=x<=5. Then use calculus to explain what you see. How…

A: Simplify the function first in order to make its graph look easier, which can be done using…

Q: Is the secant function even, odd, or neither? Is its graphsymmetric? With respect to what?

A: The given function is secant function y=secx

Q: Find ♬ as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. -["sin e de Ꮎ F(x) F(0)…

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Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

A: Given a graph of the derivative of the function f(x)

Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

A: Solution :-

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: The behavior of a function f (x) can be discovered by studying the sign of its derivative f´ (x).…

A: We will be using the information given by you. The behavior of a function f (x) can be discovered by…

Q: Let cos x if x 0 (a) Sketch the graph of f (x). (b) Is f (x) continuous at x = 0? Give reason(s)…

A: Explanation of the answer is as follows

Q: Below is the graph of f(x), f' (x), and f"(x). State which graph belongs to which function and a…

A: The f'(x) tells about the slope of the function of f(x). So if f(x) is decreasing then f'(x) < 0…

Q: Finally, to determine if Rolle's Theorem can be applied, we also need to check if the required…

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Q: Given the function f(x) = a) cos(x), 0<x</ 2x-1, 1<x< Plot the graph of the periodic extension of…

A: a) Given function is fx=cosx,0&lt;x&lt;π22x-π,π2&lt;x&lt;π The periodic extension of fx as an even,…

Q: Using the limit definition of the derivative of a function, set up the derivatives of the three…

A: We will use the definition to find the derivatives at the given values.

Q: The function f (x) is defined by the rule x2 +1 if x 2 - a) Calculate the left derivative and the…

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Q: Sketch a graph of the function f that is continuous on (-∞,∞) and has the following properties.…

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Q: The first and second derivatives of a function f are given. Use these to find the information below.…

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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.