4. Let 2x² +3 f(x) = 5 sin x X Determine if f(x) is continuous at x = 0 by computing limits. - x ≤0 2 x > 0

Q: How would you define f(7) in order to makef continuous at 7? x-2x-3 f(x) = x-7

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Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: Is there a real function f(x) that is differentiable only at a point x?

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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: 5. Let f(x) = x-3x73. Use calculus to determine the critical numbers for the function.

A: Consider the  provided function, fx=x-3x23 Find the critical point of the critical point. Find the…

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

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Q: Suppose that f(x) is a continuous function with f(-3) = – 4 and f(1) = 4. Determine which choice…

A: Consider a function f(x) defined on an interval a,b. Suppose that f is continuous and f(a)≠f(b).…

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Find c so that f is continuous at every point f(x) = 5x+12c, if x < -5 f(x) = (cx^2)+1, if x ≥ -5

A: Given- fx=5x+12c if x&lt;-5cx2+1   if x≥-5 To find- The value of c that  the above function is…

Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

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: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: 12. Let f be the function f(x)={ x² - 3bx+2; x2 For what value of b is f continuous at x = 2 ? (A) 0…

A: To find For what values of b is f is continuous at x=2.

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

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Q: Evaluate f (x): at x = -2. %D 1 - x2 Select one: A. Discontinuous B. Continuous

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Q: 20. Express the function F(x) = 1/x + J three functions. X as a composition of

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Q: Suppose that f(x) is a continuous function on the interval [0, 4] with f(0) = -10 and f(4) = 10.…

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Q: 17. Sketch the graph of f(x) = { 2x + 2, x ≤ −1 [x³−x, x>−1 and find the derivative. Determine…

A: 17. Sketch the graph of  and find the derivative.Determine whether  satisfies the conditions of the…

Q: Suppose that f(E) is a continuous function with f(– 4) = – 9 and f(0) best describes the following…

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Q: Let f(x) be the function x + 5 for x 2.

A: Let f(x)=x+5 for x&lt;-1               =cx for -1≤x≤2                =x+6 for x&gt;2 To find the…