Prove that the piece-wise function defined by 1 3x if r <-2 - - f(z) = {-4 11 2. if r = -2 %3D x² + 5x + if r> -2 is integrable on [-4, 7]. (Hint: do not use upper and lower sums, use a theorem)

Q: Which of the following is the absolute minimum value of the fuk took f(x)=(x-3)^3 on interval [1,4]

A: The graph is shown below:

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: (lx) +3, x≤-3 Q4) Check the continuity of f(x) = -2x -3<x<3 " (6x + 2, x ≥ 3

A: To check the continuity of given function,

Q: Suppose f is continuous, positive, decreasing, and concave up on the interval [5, 15]. Compare each…

A: 1) &gt; left sum will be greater than right because function is decreasing 2)  &lt; because…

Q: How are the continuous extensions often found?

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Q: 1.What is the degree of g-f inz_4[x]? Type only the numerical value if it is defined if not type…

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Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

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Q: Prove that the following function is continuous on the interval [-5,5]: H(x)= the square root of…

A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

Q: 7. has a fixed point. ) Prove that if f is a continuous function from [2, 5] to [2, 5], then f

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Q: Let /: X→Y be a function, A, B C X and C, DCY. Show that: 3. If CSD then SF (D) 4. f¹(COD)=f-¹(C)…

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Q: The psd of X(t) is given by [1+ @? for | @|<1 Sxx (@) otherwise Find the autocorrelation function.

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Q: A clamped cubic spline S for a function f is defined by 2x + x-2x Ra+ b(x -4) + c{x-4)' + d(x - 4)'…

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Q: Use 50 rectangles to approximate the are under the graph of f(x)=3** on [-2,2].

A: Area under the curve using left end points : The area under the y=f(x) over the interval a, b is…

Q: Let F ~ F4,5. Assume c₁ satisfies P(F > c₁) = 0.05 and P(F< c₂) = 0.05. Then, c₁ =_ and C₂ = (b).

A: It is given that F∼F4,5 c1 and c2 are two constants such that P(F&gt;c1)=0.05 and P(F&lt;c2)=0.05

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 i, j ∈ Za and w, x ∈ Zb with i, j different from each other and w, x different from each other.…

A: Say, the total number of elements in Za = m, the total number of elements in Zb = n,  The total…

Q: We are given the following functions f : Z → Z × Z, f(x) = (x^2, x^3).  (a) Find images f({1, 2, 3})…

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Q: f(x,y)= sin(x² + y²) + √√√9 - x² - y²

A: Note : The composition function " g∘f " of f and g  is continuous at a point "c" if f is continuous…