On the figure below, sketch the graph of a functionf that satisfies: • f is continuous, • lim f(z) = 2, • f(-1) = 0, • f"(x) <0 for z> 1, and f(r+h)-f(z) • lim h+0 < 0 for z < -3, f(z) dz <0

Q: How does the function behave as lim x → 3- for 7/(3(x-3)(5-x))?

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Q: Carefully sketch the graph of a continuous function f which satisfies the following properties:

A: Given, Sign of f'x-f'x&lt;0 on an interval -∞,-2. f'x&gt;0 on an interval -2,0. f'x&lt;0 on an…

Q: Let f(x) = x² + 3x – 2 f(x) – f(1) a) Find lim x- 1 x+ 1 b) Use your answer in part (a) to find an…

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Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: If a function f has no limit as x approaches c, then we say that lim f(x)

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Q: What is an example of a function f : [-2, 2]-->R which is not differentiable at -1 but which is…

A: To find an example of a function                                   f : [-2, 2]→R which is not…

Q: 2. Given the graph of the function f shown below, determine which of the following statements is…

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Q: Let       f(x)= 2x-2  if x0+  f(1+h)-f(1)/h Evaluate Lim h-->0-  f(1+h)-f(1)/h Is the function f…

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Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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Q: In the above space, draw the graph of a function with ALL of the following properties: (a) f(0) =…

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Q: Sketch the graph of a function f that satisfies all of the following: lim f(x) =-5 • f(-1)=2 lim…

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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.