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

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A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π &lt; t &lt; 2π.…

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

A:

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: 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…

A:

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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: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

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

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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,…

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A: Given: f(x)=1x2+1

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Q: The function f(x), which is defined for a ≤ x ≤ b, has the following behavior: f'(x) 0. Choose the…

A: Follow the procedure given below.

Q: The function, f(x), in the graph below has f(1) = 1 and f'(1) = 2. Which of the following are the…

A: