. Let f : [0, 1] R be defined by |-1, z = ; >50 f(x) = {0 |

Q: Suppose 2 < f'(x) < 6, for –1 < x< 1. Then f(1) – f(-1) is between A) 2 and 10. B) 4 and 12. C) 0…

A: GIVEN : 2 ≤f'(x) ≤6,  for -1 ≤x≤1 TO FIND : f(1) - f(-1) HINT : Mean value theorem

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

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Q: (x. v) = (0, 0)

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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: Provide concise explanations for the answers to the following: c.) Which is greater, f (2) or f…

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Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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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: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

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Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

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: (-) = { 2*. x 2 Find the values of a and b so that f will be differentiable at x = 2.

A: Given function is fx=7x2        ,x≤2ax+b    ,x&gt;2. By continuity, 722=a2+b74=2a+b2a+b=28     ...1…

Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

A:

Q: Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)?…

A: Given that f is continuous at 4,6 and that f4,y=y3 for y≠6. We have to find the value f4,6. Since,…

Q: for If f (2) is a regular function of z, prove that f (2) 2 = 4 | f'(2) 1?. %3D ve I f12) 1? =4 |…

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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: 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: 3. Let there be some a, b R such that f(a)ƒ'(a) = f(b)ƒ'(b) + 1. Show that f f(x) f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

Q: Let f (x) = vr +2² + 2 , ro = 1, h = 0.5, r1 using the Three-Point formulas to approximate f(1) (1);…

A: Given: The given fx=x3+x2+2, x0=1,h=0.5,x1=1.5 and x2=2

Q: 2. Let f(x) be a function with domain (00, -00) and f'(x) = 2x3+3x²-36r. Find the intervals where…

A: Step 1:Step 2: Step 3: Step 4:

Q: F:(- 2, 2] → R, F(x) = [, (t- 3)(f² + 1) dt

A: Given, Fx = ∫-2x2t - 3t2 + 1 dtFx = ∫-2x2t3 - 3t2 + t - 3 dtFx = t44 - 3t33 + t22 - 3t-2x2Fx = x44 -…

Q: Let f(r) = 3x² + 4x + 5 = (x),f f'(1) =

A: To find the derivative