Which of the following functions f: R → R is continuous at the point 0 € R? f(x) = { √x 0 f(x) = { {}} √(x) = { x + 2 f(x) = x² = {₁x f(x) = if x ≥ 0 if x < 0 if x < 0 if x > 0 if x < 0 if x > 0 if x ≤ 0 if x > 0 Choose... Choose... Choose... Choose... Choose...

Q: (b) Is the function f(x)=z+z+1| continuous at every z? Is it differentiable at every z? Sketch the…

A: Explanation of the answer is as follows

Q: 3. Determine if the following functions are one-one. Explain why. •f: R R f(x) = (x - 2)² ● f:R R…

A: one- one function :Let f be a function which is one one if        x1≠x2   ⇒  f(x1) ≠ fx2 for every…

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: constant k is the functionf defined by if x +0 f(x) = V5- x - V5+x k if x = 0 continuous at x = 0?…

A: On putting limit x tends to 0 when condition of not equality it becomes 0/0 form . So by…

Q: is The range of the function f(x)%= 3cos(x)+5 Select one: O a. [-3,5] O b.[-1,1] C. d.

A: The range of the function is the set of all values that f(x) takes.

Q: r what value of a is the function f (t) = 08 O-15 O -30 O 24 t -a, -10 < t ≤ 3 t² + 8t, 3 < t < 10…

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Q: For what numbers 0 is f(0) = csc 0 not defined?

A: To find the numbers θ where fθ=cscθ is not defined. Solution: We know that, cscθ=1sinθ A rational…

Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

A: Given: fx=5x2-4x+7 for x∈1, 4 To be find c∈1, 4 such that fc=13∫14fxdx Integral of ∫xndx is given by…

Q: If f:[-5, 5 ] to R is a differentiable function and if f'(x) does not vanish anywhere, then prove…

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Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

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Q: A1). Sketch the graph of ONE function such that ALL of the following hold: i). f"(x) 0 for x> 2…

A: Graph of function

Q: Let f be a function that is defined and differentiable on all of R. Here is some information about /…

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Q: Let f (x) = x3 - 6. Find all numbers c in the interval (-7, 7) for which the line tangent to the…

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Q: 8. Show that the function f(2)= 2 is continuous everywhere but not differentiable anywhere.

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Q: The function f(x) is continuous and differentiable on the interval [−2,6]. It is known that f(−2)=4…

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Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: Let f(x) = x° – 2, -1< x < 3 The domain ofƒ¯is the interval [A, B]| where A = and B =

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Q: 3. Determine whether f is differentiable or not differentiable at 1. (x – 1 if x > 1 (-x² _if x <1…

A: If a function is differentiable at any point x=a ,then its L.H.D. =R.H.D.

Q: d. For each of the following, state whether the functions f: R → R, x → f(x) are injective,…

A: Given functions: fx=3x+2 fx=3x3-7x+3 fx=x6 fx=sinx fx=0.01x fx=4 We have to check whether the…

Q: Use the graph of f to estimate where " is 0, positive, and negative. OA Zaro: x1; positive: (0,ae)…

A: Use the graph of f to estimate where f'' is 0, positive and negative:…