Compilation of Tricky Points

[8039]

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 

• The anti-derivative does not include "+c." The antiderivative of is not

[/quote]

You mean the final answer doesn't have the +c included or?

[shinny]

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral.  

• The anti-derivative does not include "+c." The antiderivative of is not

You mean the final answer doesn't have the +c included or?

It depends whether they ask for 'an' anti-derivative - which doesn't include the +c, or 'the' anti-derivative - which does.

[TrueTears]

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral.  

• The anti-derivative does not include "+c." The antiderivative of is not

You mean the final answer doesn't have the +c included or?

It depends whether they ask for 'the' anti-derivative - which doesn't include the +c, or 'an' anti-derivative - which does.

I thought finding AN antiderivative means a specific antiderivative so you DON'T need the +c

Finding THE antiderivative means finding the FAMILY of antiderivatives so you NEED the +c

:X


Yup after checking Essentials text, I've confirmed the above to be correct.

There's a mistake in the following quote from the OP:

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 

• The anti-derivative does not include "+c." The antiderivative of is not

AN = no +c
THE = NEED +c

[shinny]

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 

• The anti-derivative does not include "+c." The antiderivative of is not

You mean the final answer doesn't have the +c included or?

It depends whether they ask for 'the' anti-derivative - which doesn't include the +c, or 'an' anti-derivative - which does.

I thought finding AN antiderivative means a specific antiderivative so you DON'T need the +c

Finding THE antiderivative means finding the FAMILY of antiderivatives so you NEED the +c

:X

Whoops, yeh wrong way. I'll fix it now. Was following the wording on the quote and got messed up >< Didn't think about it myself.

[kyzoo]

...Oh wow I never knew that, thsi will help for Spesh =D

[vea]

This is the first time I've noticed this guide here, it is nicely written, thanks!

[34590]

I'm freaking out about Exam 2 next year .......... already!    OMG

[8039]

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 

• The anti-derivative does not include "+c." The antiderivative of is not

You mean the final answer doesn't have the +c included or?

It depends whether they ask for 'the' anti-derivative - which doesn't include the +c, or 'an' anti-derivative - which does.

I thought finding AN antiderivative means a specific antiderivative so you DON'T need the +c

Finding THE antiderivative means finding the FAMILY of antiderivatives so you NEED the +c

:X


Yup after checking Essentials text, I've confirmed the above to be correct.

There's a mistake in the following quote from the OP:

ANTI-DIFFERENTIATION and DIFFERENTIATION

• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 

• The anti-derivative does not include "+c." The antiderivative of is not

AN = no +c
THE = NEED +c

What a pathetic way to trick students ;(

[lovingit]

For q.4 of the sample questions put up by VCAA for the exam 1 this year
Is there a mistake in that there shouldn't be square brackets.
Also how do i know if a connecting point of a hybrid graph is differntiable or not?
Thanks

[vea]

For q.4 of the sample questions put up by VCAA for the exam 1 this year
Is there a mistake in that there shouldn't be square brackets.
Also how do i know if a connecting point of a hybrid graph is differntiable or not?
Thanks

VCAA has made no mistake, the square brackets are there to say that the function is STRICTLY decreasing at that interval. This is because a stationary point is BOTH DECREASING AND INCREASING AT THE SAME TIME (STRICTLY).

Also, you know that a connecting point of a hybrid graph is differentiable if the point is smooth. i.e. The gradient of the point is the same for both parts of the hybrid function at that point.

[lovingit]

For q.4 of the sample questions put up by VCAA for the exam 1 this year
Is there a mistake in that there shouldn't be square brackets.
Also how do i know if a connecting point of a hybrid graph is differntiable or not?
Thanks

Thanks for that,
but in Q.3a in the sample extended response questions http://www.vcaa.vic.edu.au/vce/studies/mathematics/cas/casexams.html#H2N1019B
the answers have open barckets for when the function is increasing and decreasing?

VCAA has made no mistake, the square brackets are there to say that the function is STRICTLY decreasing at that interval. This is because a stationary point is BOTH DECREASING AND INCREASING AT THE SAME TIME (STRICTLY).

Also, you know that a connecting point of a hybrid graph is differentiable if the point is smooth. i.e. The gradient of the point is the same for both parts of the hybrid function at that point.

[m@tty]

Also, you know that a connecting point of a hybrid graph is differentiable if the point is smooth. i.e. The gradient of the point is the same for both parts of the hybrid function at that point.

Yeah, this.

A good way to visualise whether a point is a cusp, and hence not differentiable, is see whether you can place more than one tangent. If this is the case then there is obviously no gradient at that point and therefore it is not differentiable.

This is just a visual alternative (though obviously not for use in working in the exam...) of the said algebraic method.

[lovingit]

If at the SP, the graph is both increasing and decrasing, why in  Q.3a in the sample extended response questions http://www.vcaa.vic.edu.au/vce/studies/mathematics/cas/casexams.html#H2N1019B
do the answers have open barckets at the TP for when the function is increasing and decreasing?

[vwinnie8]

wow thanks this guide is really nice!!