Homework assignment 1:

1. Compute the values for

4

1. 3

i=1

5 1i

1. i₌₁ 3

n

1. ³

i=1

n

1. ³

i=3

• n

1. 2k + 2k k=0 k=5
   • 2i n 2i
2. i=0 3 + i=43

n

1. (i³ +2i² i +1)

i=1

• i

1. i=5 (4i + ₅)

k j

1. (i j² 2)

j=0 i=1

m j

1. _j=1k=1(3C + k 3j +i)

j n k

1. l=4 j=1(i 4)

i=1

2. Calculate the answer (do not use any calculators) (log3=1.5)
   1. log₄ x= 5 x= ?
   2. log₃ y= 4 y= ?
   3. x= 7² log₇ x= ?
   4. x= 32 logx= ?
   5. 2log5 + 4log6 27log₃5
   6. 9log₃2 25log₅4 36log₆7 +8log₈6

210

1. log(4⁵ 8³) log(168) + log(4 2 ) 3
2. log(32 643) log(21091282 3 ) 8
3. loglog16
4. log16log16 Compare your answer with part i.
5. log216 Compare your answer with parts j and i.
6. log2 log5 625log3 log4 239 + log4 25
7. loglog₈ log256+log⁵(3²)4^log7
8. log₆ x= 5 log_x 6 = ?
9. log_y x=10 log_x y = ?
10. log₄ 32log₈² 4
11. log₄ 8₊log₉ 27log₂₅²125log₈³16₊log₄ log256

3. Compute the derivative of

a. 5x³ +2x1

1. 3x 2 x+x1/2 6x2/3 5

c.

1. logxx² lnx+lnx⁴

e.

1. ₃

4. Determine the limit of
5. lim

x

1. lim(1+3)

xx

1. lim3xlog x+2

xx3+7x

d.

e.

f.

x

1. xx lim2_x

x

1. lim xx x(2x)

x

1. log xlog x

lim x1/5

x

1. log⁴ x³ lim

x

1. x+1 lim32xxln₂x x

3

1. lim log^{ln x}(2x)

x

5. Compute the exact values for

n

1. (2x⁴ +5 x)dx
   • n

1 1

1. 1 (x⁴ 3x² + _{x x}2 )dx

n

³

1. (+ lnx+e^x)dx
   • n
2. xe^xdx
   • n
3. (xlnx 4lnx)dx
   • n
4. xsin xdx

1

6. Use mathematical induction to prove that

7. Use mathematical induction to prove that