Question

limit

Answer 1

\[(1/x- 1/5)/(x-5)\]

Answer 2

as x-> 5

Answer 3

what are the degrees of the top and bottom?

Answer 4

1

Answer 5

-1 and 1

do you recall your rules for degrees?

Answer 6

What do you mean by degree? You mean power of x?

Answer 7

yes

Answer 8

might only work for proper polynomilas tho

simplify by multiplying top and bottom by 5x

Answer 9

5-x/(5x^2-25x)

Answer 10

(5-x)/(5x(x-5))

-(x-5)/(5x(x-5))

-/(5x)

Answer 11

-1/(5x)

Answer 12

-1/25, got you

Answer 13

or we could use L'hospitals rule right?

Answer 14

Or just the definition of the derivative.

Answer 15

the fractiony top part tends to play havok with derivatives, but its worth a shot if you are allowed to use it

Answer 16

1/x derives to -1/x^2 ... and the limit thing is usually x to 0 tho

Answer 17

By looking at it, how did you come up to multiply by 5x?

Answer 18

/x and /5 have 5x as a common denomto clear the fractions

Answer 19

Got you! thanks

Answer 20

lhop has no issues with this

Answer 21

good luck

Answer 22

For \(h\to0\), where \(h\) represents the difference between two values of the independent variable.

You can make a small modification to that definition to arrive at the derivative at a point:
\[f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}~~\implies~~f'(c)=\lim_{x\to c}\frac{f(x)-f(c)}{x-c}\]