Determine a region whose area is equal to the given limit. Do not evaluate the limit. lim 5 + i= 1 Oy = x8 on [0, 2] O y = (5 + x)7 on [5, 7] O y = (5 + x)7 on [0, 2] O y = (5 + x)8 on [0, 2] O y = (5 + x)8 on [5, 7]
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- Evaluate the limit limn→∞ ∑ n i=1 f(ci ) Δxi over the region bounded by the graphs of the equations.Use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region. y = 27 − x3 , [1, 3]Find the exact area of the region under the graph of y= e -x from 0 to 2 by using a computer algebra system to evaluatethe sum and then the limit in Example 3(a). Compare youranswer with the estimate obtained in Example 3(b).
- In the given equation , use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region y = 27 - x3 , [1, 3]Use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region. y = x2 + 2, [0, 1]Use the limit process to find the area of the region between the graph ot the function and the x-axis over the given interval. y=64-x3, (2,4]
- Sketch the region and use the limit definition to find the area of the region between the graph of f(x)=x2+3 and the x-axis over the interval [0,2}. First determine (DELTA)x=____, ck=____, f(ck)=____.Use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval; f(x)=2x3+x2+3, [0,3] using sigma notationUse the limit process to find the area of the region between the graph of the function and the x-axis over the given interval. y = 16 − x2, [−4, 4]
- Use the limit process to find the area of the region bounded by the graph of the function and the y-axis over the given y-interval. Sketch the region. g( y) = 4y2 − y3, 1 ≤ y ≤ 31. Use the definition of the limit ( epsolon - delta ) to show thatlim of 1/z as z approaches -i2. Give the condition which ensure that |ez| < 1 where z in C.Use the limit process to find the area of the region between the graph of the function and the y-axis over the given y-interval. g(y) = 4y2 − y3, 1 ≤ y ≤ 3 (Show on the graph)