Determine a region whose area is equal to the given limit. Do not evaluate the limit. (2) lim tan 7n 7n i=1 O tan(x) on - tan(x) on 0, O tan(x) on [0, 7x] O xtan(x) on - Oxtan(x) on 0,
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Determine the region
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- Evaluate the limit limn→∞ ∑ n i=1 f(ci ) Δxi over the region bounded by the graphs of the equations.4. Find the limit, if it exists, or show that the limit does not exist: lim(x,y)→(1,−1) 3^−xy cos(x + y)Find the area between the graph of y=5-5x^(2/3) and x-axis and -1≤x ≤8 using the limit definition and sigma notation.
- 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 notationLet A be the area of the region that lies under the graph of f(x) = e^(-x) between x = 0 and x =4. Using right endpoints, find an expression for A as a limit. Do not evaluate the limit.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]
- Using the elpison delta defination of a limit prove that the limit of (5x+7)=2 as x approaches -1 existsFind the limit, if it exists, or explain that the limit doesn’t exist. (a) lim [(4xy)/sqrt(x^2+y^2)](x,y)→(0,0) (b) lim (x^2+2y^2)ln(x^2+2y^2) (x,y)→(0,0)Find the limit L. Then using the Epsilon Delta definition to prove that the limit is L lim x→−4 (x^2 + 4x)
- Evaluate the limit lim xi over the region bounded by the graphs of the equations. f(x) = √x, y = 0, x = 0, x = 3Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim x→0− (6+1/x)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).