Please show all work (pictures preferred, neat writing) 1) Find the number n suc

ID: 2986516 • Letter: P

Question

Please show all work (pictures preferred, neat writing)

1) Find the number n such that [(n) on top of (BIG E) under e is (i=1)] of i = 78

2) Find the limit

lim n->infinity of [(n) on top of (BIG E) under e is (i=1)] of 3/n [((1+(3i/n))^3)-2(1+(3i/n))]

3) Determine a region whose area is equal to the given limit. Do not evaluate the limit.

lim n->infinity of [(n) on top of (BIG E) under e is (i=1)] of 2/n [(5+(2i/n))^10]

4) lim n->infinity of [(n) on top of (BIG E) under e is (i=1)] of [xi/((xi^2)+4)][delta x] and the interval is [1,3]

5) evaluate the integral by interpreting it in terms of areas

integral from 0 to 10 of the absolute value of (x-5) dx

6) evaluate the integral

integral from 0 to 2 of [(y-1)(2y+1)]dy

7) evaluate the integral

integral from 1/2 to 1/(sqrt 2) of [4/(sqrt (1-x^2))]dx

8) find the derivative of the function

F(x)= integral from sqrt x to 2x of [arctan(t)]dt

9) evaluate the integral

integral from 0 to pi/3 of [(sinx+sinx((tanx)^2))/((secx)^2)]dx

10) evaluate the integral

integral from 0 to 3pi/2 of the absolute value of (sinx) dx

11) evaluate the indefinite integral

integral of [(arctanx)/(1+(x^2))]dx

12) evaluate the indefinite integral

integral of [(sin(lnx))/x]dx

13) evaluate the indefinite integral

integral of [(2^t)/((2^t)+3)]dt

14) evaluate the indefinite integral

integral of [sint((sec(cost))^2)]dt

pi/3

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