Calculus Answers

Find the limit of the sequence& &

1-& & & & Lim& (( 4 + 16n [sup]6[/sup]) / (7+ n [sup]6[/sup]))^1/4& &
& & & & & & & & & N ->& ∞

2-& & & Lim& (n[sup]2[/sup] + 3n ) /& e[sup]2n[/sup]&
& & & & & & & & & N ->& ∞

3-& & & Lim& (( 4 - n[sup]5[/sup]) / (n[sup]5[/sup] – 7 ) )[sup]1/3[/sup]& &
& & & & & & & & & N -> ∞

4-& & & Lim& ( 1 + 5n ) [sup]1/ n^2[/sup]
& & & & & & & & & N -> ∞

Evaluate the improper integral &
1-& & & ʃ& & In x& / x& & dx& & & & & & & & & & & & & & & & & & & from (& & 0& & & to& & & 4 )
2-& & & ʃ& & dx& & /& & (& 4 – x )[sup]1/5[/sup]& & & & & & & & & & & from& (& & 0& & to& & & & 4)
3-& & & ʃ& & & 1 / x[sup]2[/sup]& & & & dx& & & & & & & & & & & & & & & & & & & & & from (& & -∞& & & & & & to& -3& & ) &
4-& & & ʃ& & 1/ x[sup]4[/sup]& & & dx& & & & & & & & & & & & & & & & & & & & from (& & -∞& & & & & & to& -2& & )

Find the area of the largest isosceles triangle inscribed in a semicircle of radius 10ft., the vertex of the triangle being at the center of the circle.

Evaluate the improper integral
+∞
ʃ dx / x^3 – 4x
- ∞

evalute the improper integral

1- In x / x dx E( 0 , 4 )


2- x e^-x^2 dx E( - infinity to + infinity)

What is the integral of
& sec[sup]5[/sup] x dx ?

What is the volume and surface area of a cube with an edge length of 4 cm?

What is the integral of tan^-1(4x) dx ?

A real estate firm owns 100 garden type apartments at $400/month. For each $10/ month increase there will be two vacancies with no possibility of filling them. What rent per month will max monthly revenue?