Description

Homework assignment 1: 

1. Compute the values for

4

1. 3

i=−1

5 1_i

1.   i₌₁ 3

n

1. ³

i=1

n

1. ³

i=−3

• n

1. 2k + 2k k=0 k=5
   • 2i n 2i
2. i=0 3 + i=−43

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=1_k=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(16−8) + log(4 2 ) 3
2. log(32 643) −log(21091282 3 ) 8
3. loglog16
4. log16log16 Compare your answer with part i.
5. log216 Compare your answer with parts j and i.
6. log2 log5 625−log3 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 32₋log₈² 4
11. log₄ 8₊log₉ 27₋log₂₅²125₋log₈³16₊log₄ log256

 

3. Compute the derivative of

a. −5x³ +2x−1

1. 3x −2 x+x1/2 −6x−2/3 −5

c.

1. logx−x² lnx+lnx⁴

e.

1. ₃           

 

4. Determine the limit of
5. lim

x⎯⎯→

1. lim(1+3)

x⎯⎯x→

1. lim3xlog x+2

x⎯⎯x→3+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− _x2 )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