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To find: Describing the process of the area of region bounded by the graph of a nonnegative, continuous function
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Answer to Problem 49E
The area of region is
Explanation of Solution
Given information:
The given continuous function, the x-axis and the vertical lines
Concept used:
The Area Problem;
Let
Its area by using a geometric formula and different approach like as the limit of a summation.
Using an equal width accumulation of rectangles,
The length of the interval over the x-axis is
The area of the region bounded by the graph of
The dimensions of the n rectangles;
The width of each rectangle is.
And, obtain the height of each rectangle, evaluate
The
The right end point of each interval is
Approximate the areas as the sum of the areas of
Finally the exact area by taking the limit as
Chapter 12 Solutions
Precalculus with Limits
- Use the following graphs to evaluate the given one-sided limit. Answer exactly. y = f (x): y = g(x): 8 6 ν -8-6-4-2 2- 1-2-2 -4 -6 -8 ° 4 lim (f(x)+g(x)) = x+2+ 8 6 2 ν 0 x x 6 8 -8 -6-4-2 2 6 8 -2 -4 -6 -8arrow_forwardQuestion 1 The points A = (-2, 3, 2) and B = (4, 1, 4) are reflections of one another in a plane S. Find an equation for S.arrow_forwardThe graph below is the function f (x) -D -3-2 4 3 2 Q2 03 Find lim f(x) = x-1- Find lim f(x) = x−1+ Find lim f(x) = x-1 Find f (-1) = 3 4 5arrow_forward
- i circled the correct answer and i did most of the question but i cant figure out how to add both residues to get the correct answer could you please show me how to do itarrow_forwardQuestion 3 Starting at the point (0, −2,0), I walk up the hill z = 4-x² — y². The projection of my path on the xy plane is the line y = 2x-2. (a) At what point on my path is my altitude (the z-value) the greatest? (b) What is the slope m of my path (taking the z-axis to be vertical) when I am at the point (1, 0, 3)? [Hint: Parametrize my path (take x to be t).]arrow_forwardI circled the correct, could you explain using stokearrow_forward
- Use Euler's method to numerically integrate dy dx -2x+12x² - 20x +8.5 from x=0 to x=4 with a step size of 0.5. The initial condition at x=0 is y=1. Recall that the exact solution is given by y = -0.5x+4x³- 10x² + 8.5x+1arrow_forwardFind an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).arrow_forwardFind the point on the graph of the given function at which the slope of the tangent line is the given slope. 2 f(x)=8x²+4x-7; slope of the tangent line = -3arrow_forward
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