Limits, Sequences, and a Lil Induction

Limits

100

lim_x->-3 (6+4x)/(x²+1)

-3/5

200

lim_t->0 [(6+t)²-36]/h

12

300

lim_x->-5(x²-25)/(x²+2x-15)

5/4

400

lim_x->-3  (sqrt(2x+22)-4)/(x+3)

1/4

500

lim_x->0  x/(3-sqrt(x+9))

-6

L'H

100

lim_t->-4sin(Pi*t)/(t²-16)

-Pi/8

200

lim_t→1

(5t^4−4t^2−1)/(10−t−9t^3)

-3/7

300

Lim_x→infinity x³*e^-x

0

400

lim_{x->- infinity}  xe^x

0

500

lim_x->infinity  x^1/x

1

Limits of Sequences

100

lim_n->infinity 4ⁿ/(12ⁿ/4ⁿ)

diverges to infinity 

200

lim_n->infinity  -7ⁿ/7ⁿ

diverges

300

lim_n->infinity 12ⁿ/18ⁿ

converges to 0

400

lim_n->infinity  25ⁿ/25ⁿ

converges to 1

500

lim_n->infinity   3n+15/n

3

Induction

400

Prove that 1+3+5+...+(2n-1)=n²

See Micah

500

Prove 2+4+6+...+2n=n²+n

See Micah