Need help with these problems!

[aws41109]

I really cannot start to figure these problems out!


If ∫ (x²-2x+2) dx [0,6] is approximated by three inscribed rectangles of equal width on the x-axis, then what is the approximation?
Let f(t)= 1/t for t>0. For what value of t is f’(t) equal to the average rate of change of f on the closed interval [a,b]?
(A) -√(ab) (B) √(ab) (C) -1/√(ab) (D) 1/√(ab) (E) √((1/2)(1/b-1/a))


What is: lim (x->b) (b-x)/(√(x) - √(b))



t: 1 3 6 10 15
f(t) 2 3 4 2 -1

The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x]. Using the intervals [1,3], [3,6], [6,10], [10,15], what is the approximation of g(15) – g(1) obtained from a left Riemann Sum?

 

[Deleted member 4993]

I really cannot start to figure these problems out!


If ∫ (x²-2x+2) dx [0,6] is approximated by three inscribed rectangles of equal width on the x-axis, then what is the approximation?

First plot this function (x² - 2x + 2) approximately

If want to use three inscribed rectangles to approximate the area under the curve (function) - then what would be the width of each rectangle?

Let f(t)= 1/t for t>0. For what value of t is f’(t) equal to the average rate of change of f on the closed interval [a,b]?
(A) -√(ab) (B) √(ab) (C) -1/√(ab) (D) 1/√(ab) (E) √((1/2)(1/b-1/a))


What is: lim (x->b) (b-x)/(√(x) - √(b))



t: 1 3 6 10 15
f(t) 2 3 4 2 -1

The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x]. Using the intervals [1,3], [3,6], [6,10], [10,15], what is the approximation of g(15) – g(1) obtained from a left Riemann Sum?

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