Describe how the following functions are built out of the basic continuous functions. Identify points where they might not be continuous. a(t) = t² if t > 0 and 0 if t = 0.

Q: Is the function f(x) = > ` continuous at x = 0? Explain your answer. n=0

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Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given: The function, f(x) = 10-8e9-x,  x > 910-89x,       x≤ 9

Q: Compute the right-hand and left-hand derivatives as limits to show thatthe functions in Exercise are…

A: The definitions of the left-hand side derivative and right-hand side derivative can be used to show…

Q: Determine whether the given functions are continuous or not at the indicated points. g(x)={x+ex  ;…

A: Limit                Let D c R  ,  f : D → R  be a function ,  Let c be a limit point of D . A near…

Q: f(x)=210, where is it continuous?

A: Given: fx=210 We know that graph of given function is horizontal line for every value of x

Q: Describe the interval(s) on which the function is continuous.

A: Consider the piecewise function  f(x)=x2-1x-1,              x≠12,                      x=1 To check…

Q: x² - y² z = g(x, y) = x² + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

A: Given function is z=gx,y=x5−y5x4+y4 for x,y≠0,00            for x,y=0,0. We have to check whether…

Q: Describe the interval(s) on which the function is continuous.

A: Given: Describe the interval(s) on which the function is continuous. f(x)=sec πx4Clearly from the…

Q: Determine whether the following function is continuous at the given point z За? + 14г — 5 1 f(x)= 3x…

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Q: 4 – t if t 2

A: f(t)=4-1/2t if t<2 f(t)=t+c if t≥2

Q: Where is the function f(r, y) = x/y continuous?

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Q: Find the values of a and b such that f is differentiable at r = 3 and then sketch the graph of f if

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Q: (c) Determine whether the following function continuous at point (0, 0). Justify your answer. x'y…

A: Solved below

Q: Use the three step process to determine if the function f (x) = S2² +1 ifx 2 at r = 2. Your Answer:

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Q: Suppose f is a continuous function where f(7) = 9 and f'(7) = 6 . The tangent line to the graph of y…

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Q: Determine whether the following function continuous at (0,0) or not: 4x?y x² + y² f (x,y)

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Q: Find a value of x, if any, at which f(x) = Vx – 27 is not continuous.

A: f(x) = (x-27)(1/3) To find :- Value of x where function is discontinuous

Q: At what points are the functions continuous? x tan x y = x² + 1

A: Given function is y=xtanxx2+1.

Q: For the function f(x, y) below, determine whether there is a value for c making the function…

A: Given function,   f(x, y) = c + y        x≤46 - y        x>4 c = ?

Q: At what points are the functions continuous? y = x tan x/x2 + 1

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Q: Compute the right-hand and left-hand derivatives as limits and check whether the function is…

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Q: Consider the following. S-3x, f(x)={2 - 2x+ 9, x > 2 Find the x-value at which f is not continuous.…

A: We will find the value of x at which the f is not continuous and whether the discontinuity is…

Q: (x, y) = (0, (x, y) = (0,

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Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

Q: xy? x2 + y4' (x, y) # (0,0) f(x, y) = 0, (x, y) = (0,0)

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Q: Find the value of the constant c that makes the following function continuous on (−∞,∞). f(x)={x^2−c…

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Q: Determined where the function f(x) is continuous

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Q: Where is f(x) = e* continuous?

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Q: f (x) = v2 – x at x = 1

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Q: Is the function given below continuous/differentiable at x = 3? %3D -3x + 2 x 3

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Q: . Determine the value of c such that the function remains continuous. Draw your resulting function…

A: If the given function f(x) is continuous then the left-hand limit, right-hand limit and value of the…

Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

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Q: At what points of R? are the following functions continuous?

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Q: f(x) = (xsin(x),ifx T.

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Q: Find the intervals on which the function f(x)=e1/x is convex upward and convex downward.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

Q: Compute the right-hand and left-hand derivatives as limits to show that the functions are not…

A: y=x,  y=1x  &  P1, 1. Left hand derivative is,…

Q: Compute the right-hand and left-hand derivatives as limits and check whether the function is…

A: NOTE: Refresh your page if you can't see any equations. . the definition of derivative is  find the…

Q: Determine whether the following function is continuous at the given point z= 22 +9z – 5 f(=) = 2x-1…

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Q: At what points of R² are the following functions continuous?

A: A function is not continuous at the value of variables when the function does not give a defined…

Q: Is the given statement true or false? Justify your answer. 'If the function f is continuous at a,…

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Q: At what points is the function f given by f(z) = x3 + i(1 + y) analytic? Explain.

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Q: Determine the set of points at which the function is continuous. F(x, y) = (xy)/(1+e^x-y)

A: A function is said to be discontinuous if it is not defined at a certain point  For the function…

Q: Is the given function f (x, y, z) = xª – 6xy? + 723 continuous at the origin? Yes No

A: If a function f and another function g is continuous at arbitrary point. Then there sum, difference…

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (a²² + y² – 4)

A: Given function is                                                              f(x, y)=ln(x2+y2-4)…

Q: The function f(x) = k is continuous.

A: Given f(x) = k

Q: Is the signum function, f(x) = sgn x, continuous at x = 0?

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Q: Find the intervals on which the function f(x)=e−x3 is convex upward and convex downward.

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Q: Define for a function rasls, y. 2) - slelo), 0), alo) where and, are differentiable functions.

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Q: Graph the function and observe where it is discontinuous. f(x, y) = e1/(x - y) fis discontinuous at…

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Q: (а) f(х) — х — 1; 1%3D[-2,2] (b) ƒ(x) = x² – 5; I = [-5, 5] (с) f (х) — 2* — х+1; I%3D (2, +o0) -

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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.