3. How is the continuity of the following function at x=0? There exist Left continuity Right continuity x−|x| x = 0 r=0 . Does not exist f(x) = 8 (1

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A: Explanation of the answer is as follows

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: Investigate the continuity of the following function S(2) = if z +0 if z = 0 (i) Is f(z)…

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Q: Test the continuity of the following lons at tne points each (x+1, 3x- 1, 1 < x < 2; (i) x= 1, (ii)…

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Q: If f(x) = g(x) for x # c and f(c) # g(c) then either f or g is not continuous at c.

A: Continuous Function:In mathematics, a continuous function means that a continuous change in the…

Q: (x+2, x ≤ 1 (B)Test the continuity of the function f(x) = {4-x, x>1, at x=1. 6

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Q: If f(x) = 1+ then the interval(s) of decreasing is(are) Select one: O (-00,-1]U[1, 0) O -1,0) U (0,…

A: f(x) = x + 1x Differentiating with respect to x: f'(x) = 1 - 1x2   .......................using…

Q: Q5: State and prove the theorem of (continuity-differentiability), then find the value(s) of x that…

A: As per the policy, we are solving first question. Please repost the question and specify which…

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A: Given, f(x) is a continuous function satisfying the following table.   -∞,-6 -6, 1 1, 3 3, ∞…

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Q: f(x) is a function with the domain (-00, -7) U (-7, 3) U (3, 0), and the graph of given below (1.e.,…

A: Given, fx is a function with domain -∞,-7∪-7,3∪3,∞ and the graph of f''x is

Q: Investigate the continuity of the following function f(2)= if z +0 if z =0 (i) Is f(z)…

A: Calculate the limit:

Q: (f) The function f(x) = √√x is differentiable at x = 0. ○ True O False

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: (ii) Investigate the continuity of the following function f(2) ={ if z +0 if z =0 (iii) Is f(z)…

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Q: nctions at the indicated points of each (i) x = 1, (ii) x = 2 and x = 3/,.2(

A: f is continuous at x = 1 f is not continuous at x = 2 f is continuous at x = 3/2   The detailed…

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Q: (Change-of-variable Formula). Let g : [a, b] → R be differentiable and assume g is continuous. Let…

A: Given: g: a,b→R is differentiable and g' is continuous. Also, f:c,d→R is continuous and the range of…

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A: f(x)=|x-1|+|x+1|, for all x∈ R, It can be written as f(x)=-(x+1)-(x-1),       x&lt;-1(x+1)-(x-1),…

Q: The graph below shows the derivative of the function y=f(x) on the interval € [0, 8]. Suppose f(x)…

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