[ f(x) dx 3 Given that 1 ≤ f(x) ≤ 4 for 3 ≤ x ≤ 7, estimate the value of ] ≤ [ f(x)da <

Q: Let X={1, 2, …, 16} and define function f(x)=rx for all x€X where rx is the remainder when 3x is…

A:

Q: Is it possible for a function to satisfy f(x) &gt; 0, f′(x) &gt; 0, andf ″(x) &lt; 0 on an interval?…

A: We want function that is: 1. positive on interval I since fx&gt;0   2. increasing on interval I…

Q: Find the domain and range of the function g(x, y) = x√y

A: Given , gx,y=xyNow , x∈R , y&gt;0 i.e y∈R+∴ Domain .    x,y/x∈R , y∈R+…

Q: Apply Rolle's theorem for the function f(x)-x2+2x over the interval [-2,0]. Justify your answer.

A: Rolle's theorem is used to prove the Taylor's theorem and the mean value theorem. Rolle's theorem…

Q: S(r) = In (x² + 2x + 5)

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Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

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Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: Determine the intervals on which the function f(x)=e√x is convex upward and convex downward.

A: We find f"(x)

Q: For the function, find the interval(s) for which f'(x) is positive. 2 f(x) = x³+4 + 4x² - 24x+8 OA.…

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Q: 15 10 8 10 Evaluate f(0) (a) Estimate f(4) (b) 00 2.

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Q: for x 0

A: fx=x,x&lt;0x2,x≥0 ;x∈-1,1 graph of given function on given interval can be drawn as below

Q: Verify Rolle's theorem for the function 2x2 – 18x + 29 on the interval f(x) = [2, 7].

A: Given,          The function is fx=2x2-18x+29 on the interval 2,7.

Q: Let f(x) be the function 1. Find the following: x + 1 f(6) f(- 6) = 1 11 11 12 (-) 1/5

A: Given, f(x)=xx+1-1 and we have to find the value of f-12 Concept used: BODMAS rule and simple…