# D Transcribed Image Text: (a) Use the definition of the derivative to prove C=0 and da T = 1. %3D (b)

Excerpt |
---|

(0, 00), m E Z, n E N. %D – dr tn (f) Use the fact that if {tn} is a sequence in R, then lim lim r to prove that dr = trt-1 for all r E (0, o), t E R \ Q. |

D Transcribed Image Text: (a) Use the definition of the derivative to prove

C=0 and

da

T = 1.

%3D

(b) Use induction and the Product Rule to prove

I = nI”-1 for all n E No-

(c) Use the Quotient Rule to prove

= na”-1 for all I ER\{0}, n E Z\ No.

dr

d

(d) Use the Inverse Function Theorem to prove

d.x

1

= =r/n-1 for all r E (0, 00), n E N.

d.

(e) Use the Chain Rule to prove

m/n

/m-1 for all x E (0, 00), m E Z, n E N.

%D

–

dr

tn

(f) Use the fact that if {tn} is a sequence in R, then lim

lim r to prove

that

dr

= trt-1

for all r E (0, o), t E R \ Q.

### Need your ASSIGNMENT done? Use our paper writing service to score better and meet your deadline.

Click Here to Make an Order Click Here to Hire a Writer