Function Notation And Limit (1 Viewer)

[nrlwinner]

I seem to have real trouble doing this function notation question:

Find the values of b if f(x) = 3x^2 -7x +1 and f(b) = 7

Also, how do you solve limit equations with more than one pronumeral

ie.

lim as h approaches 0

lim as h approaches 0

lim as x approaches c

 

[hermand]

answers attached, excuse the random naming.

EDIT; last answer should be 3c^2, not 3x^2.

 

[Drongoski]

Limits as taught in the NSW HSC is superficial, and quite understandably. For instance:





Question: u cancelled the common factor (x-c) and u can do that only when x-c =/= 0 i.e x =/= c

How do u justify that ?

 

[hermand]

Limits as taught in the NSW HSC is superficial, and quite understandably. For instance:





Question: u cancelled the common factor (x-c) and u can do that only when x-c =/= 0 i.e x =/= c

How do u justify that ?

because x doesn't actually equal c, it just approaches c.

 

[Drongoski]

hermand:

u've got the general idea but majority just cancel the common factors as that's how they are taught and that makes such exercises easy. Because teaching limits more in-depth is quite hard it's left out of syllabus I guess. Some intro to limits reqd to help understand the process of differentiation & integration.

By the way shouldn't answer to last be 3c²

 

[hermand]

hermand:

u've got the general idea but majority just cancel the common factors as that's how they are taught and that makes such exercises easy. Because teaching limits more in-depth is quite hard it's left out of syllabus I guess. Some intro to limits reqd to help understand the process of differentiation & integration.

By the way shouldn't answer to last be 3c²

yeahh, i know what you mean. most people just do what they're told because the teachers tell them to. that's the beauty of the extension two course, it's more self-orientated and you have to understand how things work more. it's still not entirely independent though because it's still teacher-driven. if you get what i mean.

yeah it should be, but i just put x in accidentally instead of c. should write that above.

 

[nrlwinner]

hermand ur a genius

Edit. I got another question I'm stuck on.

If f(x) = 2x -1, show that f(a^2) = f(-a^2) for all real a.

 

[Drongoski]

hermand ur a genius

Edit. I got another question I'm stuck on.

If f(x) = 2x -1, show that f(a^2) = f(-a^2) for all real a.

This can't be right.

Are u saying: f(a²) = f( (-a)²) ?

If that is the case, it's true for any f(x).

 

[hermand]

hermand ur a genius

Edit. I got another question I'm stuck on.

If f(x) = 2x -1, show that f(a^2) = f(-a^2) for all real a.

that question doesn't work, because you end up with 1=-1 which isn't correct. or you might mean what drongoski said?

can you please write it out and scan it or use the equation editor so i can see the question as it's written in the book?

thanks.