Limit of (√6(a+h) - √6a) / h as h approaches 0 in terms of constant a

[cdaw784]

Homework Statement

Find in terms of constant a

lim (√6(a+h) - √6a) / h
h→0

The Attempt at a Solution

I've tried multiplying by the conjugate [√6(a+h) + √6a] but I still can't seem to get the right answer.

Any help would be appreciated.

 

[Mark44]

Homework Statement

Find in terms of constant a

lim (√6(a+h) - √6a) / h
h→0

The Attempt at a Solution

I've tried multiplying by the conjugate [√6(a+h) + √6a] but I still can't seem to get the right answer.

Any help would be appreciated.

Show us what you tried. You can't just multiply by the conjugate - you have to multiply by the conjugate over itself. Show us what you did and we can steer you in the right direction.

 

[Mark44]

Also, don't post a problem in more than one forum section. This is the right place - I deleted your other post of this problem.

 

[cdaw784]

well,

I've multiplied both the top and bottom by the conjugate which would then equal,
6(a+h)-6a / h(√6(a+h) + √6a)

which i then get,
6a+6h-6a/ h(√6(a+h) + √6a)

but then the whole thing just equals 0 and I'm lost.

am i correct or wrong so far?

 

[Mark44]

well,

I've multiplied both the top and bottom by the conjugate which would then equal,
6(a+h)-6a / h(√6(a+h) + √6a)

which i then get,
6a+6h-6a/ h(√6(a+h) + √6a)

but then the whole thing just equals 0 and I'm lost.

am i correct or wrong so far?

No, the whole thing doesn't equal 0.

What do you get when you simplify this? (6a+6h-6a)/ [h(√6(a+h) + √6a)]
Note the added parentheses and brackets.

After you simplify it as much as possible, then take the limit as h → 0.

 

[cdaw784]

so,

(6a+6h-6a)= 0a+6h= 6h

and

[h(√6(a+h) + √6a)]= (h√6(a+h)) + (h√6a)

which would mean,

6h / [(h√6(a+h)) + (h√6a)]Should I separate (h√6(a+h)) into [h√6a + h√6h] or no?

 

[cdaw784]

i ended up doing,

6h / h (2√6a) + (√6h) and than cancel out the h

= 6 / (2√6a) + (√6h) and then multiplying (2√6a) + (√6h) to top and bottom to get rid of sqrts

= 6 [(2√6a) + (√6h)] / 12a+6h = 12(√6a)+6(√6h) / 12a + 6h

if i plug in 0 for h i get,

12(√6a)+6(√6(0)) / 12a + 6(0)
= 12(√6a) + 0 / 12a + 0 = 12(√6a) / 12a

now i simplify the 12/12 into 1/1 = (√6a) / a

however when i plug in (√6a) / a as my answer, it is incorrect.

am I still wrong?wait a minute i figured my mistake,

2(√6a)*2(√6a) = 24a not 12a...

after transferring 24a for 12a and re-doing my work the answer i come up with is,

6(2(√6a)+(√6h)) / 24a + 6h = 12√6a + 6√6h / 24a + 6h

substituting 0 for h i get,

12√6a + 6√6(0) / 24a + 6(0) = 12√6a / 24a

simplifying gives me,

√6a / 2a

 

[Dick]

So far, you are correct with 6h / [(h√6(a+h)) + (h√6a)]. Now what do you get when you cancel the factor of h in the numerator and denominator? You are making a lot of algebraic mistakes.