- #1

- 1,316

- 104

In previous threads, I have asked about sine and cosine. The answer given by the members/mentors/advisor are very clear. But lengthy. Perhaps these yes/no questions that I can simply remember and not forget it (again).

So here we are

1. if h = 0 then sin(h)

**=**0

2. if ##\lim_{h \to 0}## then sin(h)

**≠**0

3. If ##\lim_{h \to 0}## then sin(h) has

**no**limit

4. if h = 0 then sin(h)/h is

**undefined**

5. if ##\lim_{h \to 0}## then sin(h)/h

**=**1

6. If ##\lim_{h \to 0}## then sin(h)/h

**has**limit

7. if h = 0 then Cin(h)

**=**1

8. If ##\lim_{h \to 0}## then cos(h)

**≠**1

9. If ##\lim_{h \to 0}## then cos(h)

**has**limit

---------------------------------------------------------------------

10. if ##\lim_{h \to 0}## does cos(h) - 1 has limit? If yes then what is the value?

11. if ##\lim_{h \to 0}## does (cos(h) - 1)/h has limit? If yes then what is the value?

And in the derivative of Sin(x)

##\lim_{h \to 0} \sin(x)\frac{\cos(h)-1}{h} + \cos(x)\frac{\sin(h)}{h}##

##\lim_{h \to 0} \sin(x)\frac{\cos(h)-1}{h} + \cos(x)##

So if the derivative of Sin(x) is Cos(x) then...

##\lim_{h \to 0} \sin(x)\frac{\cos(h)-1}{h}## should be zero. then...

12. ##\lim_{h \to 0} \cos(h)-1## should be zero, then...

13. ##\lim_{h \to 0} \cos(h) ## should be 1, then...

8. If ##\lim_{h \to 0}## then cos(h)

**≠**1

It seems number 13 contradicts number 8.

I would be very grateful if someone be sokind to answer me. But before that, could you confirm the yes/no question in number 1 to 9, please.

Thank you very much.