O g(x)= ( % x + %) X so at the point X, =O. x >0 9メ- x

Q: How is a function’s differentiability at a point related to its continuity there, if at all?

A: If a function is differentiable at any point there it has to be continuous. For example: y= x^2 has…

Q: What is the common way to obtain a new function from an existing one?

A:

Q: Show that the general solution of the equation 4,32.xy°u, = 0 is given by where f is an arbitrary…

A:

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

A:

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: Question 22 is about differentiate the function

A: To differentiate with respect to variable x,

Q: ex-1 if x + 0 (a) f(x) = log(1+2x)' 1 if x = 0 2 at x = 0 |x²-1| for x # 1 at x = 1 (b) f(x) = %3D…

A:

Q: x rational 0, x irrational. x. g(x) =

A: We have to find

Q: Sketch the graph of the function as attached. (a) Evaluate f(1), f(0), f(1/2), and f(−2.7) (b)…

A:

Q: Discuss continuity of a function at a number a. Provide two examples showing continuity at a number…

A: CONTINUITY A function f(x) is said to be continuous at some point x=a if for every ε&gt;0 ∃ δ&gt;0…

Q: What does it mean for a function to be defined implicitly by an equation?

A: An implicitly defined function is a function that is presented as the solution of some equation or…

Q: C. Discuss the continuity of the following functions at/on the given point/interval. 4x 1. (6…

A: Continuous

Q: G(x): x³+3x+2 x+2 [[_x_]] + 1 -12-X1 - x+3 + 1 x-r if x < -1 if -1 ≤ x 1 if xz1

A:

Q: Give one way to restrict the domain of the function f (x) = X4-2to make the resulting function…

A: Given function is: fx=x4-2fx=x2

Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

A:

Q: About the Discontinuity of a function, kindly provide 5 Questions about it with solutions.

A: For a function f(x) to be continuous at a point x=a, it must satisfy the two of the following…

Q: The cost C in dollars of manufacturing x bicycles at a production plant is given by the function…

A: topic- application of derivatives

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

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

A:

Q: Aen vity # 2 BLs auss ME! t) flx):1 Xスー 2.

A:

Q: x + 1, x2 – 2x, f(x) =3 e*, x 2 (log(5 + x),

A: We have to determine the  continuity of given function.

Q: Show that Rolle’s theorem is false for the function f(x) = |x| on the interval [−2, 2]. How can a…

A: Given function f(x)=|x|interval [-2,2] We apply Rolle's theorem only when the function is continuous…

Q: A function has a zero at X = 8, indicating what?

A: Given, A function has a zero at X=8

Q: The graph of which function starts at (0,0)?

A: The graph of the function, y = √x starts at (0,0)