True or False, and give a short reason: (a) If a function is differentiable, then it is continuous. (b) If a function is continuous, then it is differentiable. (c) If f is continuous on -1, 1] and f(-1) 4 and f(1) = 3, then there is an r=r so that f(r) = . (d) If f is continuous at 5, and f(5) = 2, then the limit as r 2 of f(4r - 11) must be 2. %3D Al1

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

A:

Q: But the Mean Value Theorem only applies if the function is continuous AND differentiable.  Not…

A: For Mean value theorem, function should be differentiable on open interval (a,b) and continuous on…

Q: Show that the function f(z)= Im(z) is nowhere differentiable.

A:

Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

A:

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 is IR? \ {(0,0)}. 22 + y2 The domain of the function f(*, y) True O False

A:

Q: (3-x, xs1 Consider the function given by f (x) = Is the function continuous, %3D x -x+1, x>1…

A:

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

A:

Q: 5. Ôx (@) = ¢x (- w), if X is symmetric function.

A:

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

A:

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: Which of the following statements is false for a function f that can be differentiated at least…

A: We have to define which statement is wrong

Q: for a -1 2x +5 f (x) = If fis the function defined above, then f' (-1) is A -2 B 3. E) nonexistent…

A:

Q: If a function f is not differentiable at x = a E R, then f is not a differentiable function. True O…

A: The given statement is if a function f is not differentiable at x=a∈ℝ, then f is not a…

Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: For questions 8-10, let f(x) be a function defined everywhere such that f"(x) = 3x² – 12x. What are…

A: Definition used -                   Point of inflection - A point where the concavity of graph of…

Q: Let f(x, y) = Evaluate f(5,5) 175 - 3x² - 4y2

A:

Q: ery differentiable function y = f(x) defined on an open interval (a, b) has an absolute max nimum.…

A: Given problem is :

Q: Which of the following statements are true? There can be multiple true statements; indicate all of…

A: