help please!

[alaskanbullworm]

Simple but can’t figure it out

 

[Harry_the_cat]

So do you know the limit definition?

 

[Steven G]

For your case there are two definitions you could use. Can you pick one and post your work so that we know where you need help.

 

[doctorcheck]

So do you know the limit definition?.....yes

Simple but can’t figure it out....see below

To find f'(1) using the limit definition we must find
Lim as h approaches 0 of [f(1+h) - f(1)]/h for the function 10x^2 - 3
So Lim(h->0) [10(1+h)^2 - 3 - (10*1)^2] - 3]/h
Lim(h->0) [10(1 +2h +h^2) - 3 - (10 - 3)]/h
Lim(h->0) [10 + 20h + 10h^2 - 3 -10 + 3]/h
Lim(x->0) [20h + 10h^2]/h
Lim(x->0) [20 + 10h]
20
ok?

 

[Steven G]

To find f'(1) using the limit definition we must find
Lim as h approaches 0 of [f(1+h) - f(1)]/h for the function 10x^2 - 3
So Lim(h->0) [10(1+h)^2 - 3 - (10*1)^2] - 3]/h
Lim(h->0) [10(1 +2h +h^2) - 3 - (10 - 3)]/h
Lim(h->0) [10 + 20h + 10h^2 - 3 -10 + 3]/h
Lim(x->0) [20h + 10h^2]/h
Lim(x->0) [20 + 10h]
20
ok?

Try using some equal signs.
Also can you please read our guidelines so you know what type of responses to make to students. Thank you.

 

[Harry_the_cat]

Alaskanbullworm? doctorcheck?
Doctorcheck, I'm not sure how much you have helped Alaskanbullworm. Sure you've given him/her the answer, but do they understand??

 

[Deleted member 4993]

To find f'(1) using the limit definition we must find
Lim as h approaches 0 of [f(1+h) - f(1)]/h for the function 10x^2 - 3
So Lim(h->0) [10(1+h)^2 - 3 - (10*1)^2] - 3]/h ..........................incorrect
should be:

Lim(h->0) [10(1+h)^2 - 3 - {10*(1)^2 - 3}]/h

Lim(h->0) [10(1 +2h +h^2) - 3 - (10 - 3)]/h
Lim(h->0) [10 + 20h + 10h^2 - 3 -10 + 3]/h
Lim(x->0) [20h + 10h^2]/h
Lim(x->0) [20 + 10h]
20
ok?

 

[doctorcheck]

So do you know the limit definition?

Try using some equal signs.
Also can you please read our guidelines so you know what type of responses to make to students. Thank you.

Alaskanbullworm? doctorcheck?
Doctorcheck, I'm not sure how much you have helped Alaskanbullworm. Sure you've given him/her the answer, but do they understand??

My bad...I didn't read the TOS prior to answering my first question. Over at Quora, you are supposed to answer student's questions or give hints (your choice)

 

[pka]

Here is a second form of the derivative definition.
\(\mathop {\lim }\limits_{x \to {x_0}} \frac{{f(x) - f({x_0})}}{{x - {x_0}}}\)
In this case: \(\mathop {\lim }\limits_{x \to {1}} \frac{{f(x) - f({1})}}{{x - {1}}}=\mathop {\lim }\limits_{x \to {1}}\) \(\frac{(10x^2-3) - (7)}{x - 1}=?\)

 

[doctorcheck]

simplify, factor, divide then things will clear up. Ok is that a good hint or was it too much?

 

[Deleted member 4993]

simplify, factor, divide then things will clear up. Ok is that a good hint or was it too much?

Since the OP did not show any "effort" towards solution - we would not know the depth of his/her knowledge.

So the first question to the OP should be "do you know the definition of derivative using limit?

After that is clarified - then the question should be - how can we apply that definition to the current problem?

Then your instruction - simplify, factor, divide then things will clear up - becomes an excellent hint.

 

[doctorcheck]

Since the OP did not show any "effort" towards solution - we would not know the depth of his/her knowledge.

So the first question to the OP should be "do you know the definition of derivative using limit?

After that is clarified - then the question should be - how can we apply that definition to the current problem?

Then your instruction - simplify, factor, divide then things will clear up - becomes an excellent hint.

OK thanks...I now understand the limits of the help I am to give.