x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1

Q: Modify the graphs of the functions ƒ and g as shown to obtain functions that are continuous on 3a,…

A: Given that the graph of functions y=fx and y=gx are given. We have to modify the graphs of the…

Q: Determine the discontinuities of the following functions and state why the function fails to be…

A: f(x)=x3+x2-17x+15x2+2x-15function is undefine when x2+2x-15 is become 0Let…

Q: I do not understand how to find limits in a function... at all...

A: Plug the given number x which is approaching in the function.

Q: 5) If f is an everywhere differentiable function, show that 2. flxiy) = X-Y satisfies the partial…

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Q: Indicate whether f(x) is increasing or decreasing (from left to right) between each of the following…

A: From A to B:   The function is increasing, as x increases from left to right, the value of y also…

Q: If f(z) <0 for all real numbers z then f is decreasing on (-o, 00) Select one: O a. False O b. True

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Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

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Q: Determine the values of x for which f(x) is discontinuous.

A: For x&lt;=3, f(x)=3x-12 is continuous

Q: 7x5 - x3 + 2x - 5 7. lim x→-o 9x6 – 2x2 + 10

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Q: ch that the function X-4 x 5. f (x) =

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Q: 6. Determine all values of x at which the function is discontinuous. x2- 2x +5 f(x) = x2-4x 0, 4 O…

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Q: Cx² f(x) = = if x 1 { 6 C-X

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Q: Which of the following statements must be true for a function that is concave up everywhere?

A: Which of the  following must be there for a function than is  concave up everywhere .

Q: lim x² + kx Vx2 + x Ck = - x→+∞

A: Given: ck=limx→∞x2+kx-x2+x For evaluating given limit, we multiply and divide given expression with…

Q: Is the following statement correct? The continuity of the function f does not depend on the choice…

A: Continuity of function

Q: x + 2, 4. If g(x) = }VT6 – x² - 4 4 4.a) lim g(x) x-4 4.b) lim g(x) X-4 4.c) lim g(x)

A: Given function is: gx=x+2,  x&lt;-416-x2, -4≤x≤44-x,  x&gt;4     4(a) To find the value of limx→-4gx

Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

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Q: f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c…

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Q: 4. List the zero(s) of the following function: zero(s):

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Q: Let P(x0, y0) be an arbitrary point on the graph of f that f′(x0) ≠ 0, as shown in the figure.…

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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.