why the function is continuous at every number in its domain. State the domain.

Q: Continue the graph of f to the interval [−4, 4] as an even function.

A: In order to get the graph of the even function from the given graph, reflect the graph of function…

Q: 0,x1 (x+2,x<-1 10. f(x)= %3D 2,x2-1

A: Answer

Q: for - 1<x<1. Prove that for the inverse cosine function, (cos- x) = dx 1-x

A: Here, the objective is to prove the following:  ddxcos-1x=-11-x2   -1&lt;x&lt;1

Q: Find the value of the constant k that makes the function continuous.

A: Given: h(x)=3x2+2x-8x+2 if x≠-23x+k            if x=-2

Q: Find the domain of the function. 29) f (x) = v25 – x2 30) f (x) = 3x + 4 31) h(x) 32) h(t) = |t + 1|…

A:

Q: Given f(x) = x² + 2x and f+g, f-g, fg, and g(x) = 6 - x², find f g

A:

Q: What is the domain of the function f(x) =0 in set notation and in interval notation? Drag and drop…

A: Consider the given function. fx=x2-36x+6 Domain is the set of all possible input values which makes…

Q: Questiun 4 At which interval is the function decreasing? 10 10 O (7,22) O (7,9) O (0,3) O (9,22)

A:

Q: Find all the numbers for which the function is discontinuous.

A: A function is discontinuous at a point if the functional value is not defined at that point. There…

Q: Determine the value the constant a for which the function g(x) is continuous at x=1 9(x)=√x² +5x + 2…

A:

Q: n C(x) = x³ – 4x² + 9x + 60.

A:

Q: Find the absolute extrema of the function f(x)%3D on the interval[-1,1]. Vx +7 The absolute maximum…

A: Given that  f(x)=6/(√(x^2+7)) To find the absolute extrema

Q: Over what intervals of the domain is the function positive? Negative?

A: From the given graph, it is observed that the domain of the graph is -∞,∞.

Q: Explain how to determine whether a function is continuous at a number.

A: Given: Condition of whether a function is continuous at a number

Q: -10 o N 2 -10 8 10 12 14 MacBook A

A: Let,  A and B are two non-empty sets. A function f:A -------&gt; B is an assignment which assign…

Q: 0,x1 x+2,x<-1 f (x)= %3D 2,x2-1

A: Interval notation is a way to describe continuous sets of real numbers by the numbers that bound…

Q: 2x if x 2

A: This is a problem of limit and continuity. Function is called as continues if it's left and right…

Q: f(x) = 5x - 5

A:

Q: Choose the interval where the function is positive. -4 -6 -2 2 2 4 -6 -00 < < 00 0<< 00 C -2 <<2 -00…

A:

Q: Is this function Discrete, continuous, piecewise, or linear?

A: as we can see here graph does have scattered points so the given function is not Discrete. now, as…

Q: Construct a function that is undefined at points 2,3 and T.

A:

Q: Give some examples of functions that are not continuous and state the values of x for which they are…

A: Few examples are given witch is not continuous.

Q: When is the function said to be real-valued?

A: The function is said to be a real valued function if it assigns a real number for each input value…

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.