Calculus Finals Review: Seeking Tutoring/Help

[hodeez]

Ok, so I have my Calculus Finals this coming Thursday, and I hope I receive some "tutoring" or review. The teacher sent out a review sheet via email, and I mirrored it www.hodeez.com/max3_finals.doc[/URL]

Just need a little/some help on 1,4,6,7,10 and the long problem.

Of course I know the rules and I'll show you my work first, but as of right now, I'm at work and my cable @ home keep disconnecting me. So I'll brief what I can get by today hopefully :)

 

[himanshu121]

For Prob 4

f(x)= |2x+3|-|x-4|

draw the no line

------------------------------------------------------------
                     |           |           |
x                  -3/2          0           4
                       |                     |
f(x)= -(2x+3)-{-(x-4)} | 2x+3 -{-(x-4)}      | 2x+3 -(x-4)     
                       |                     |

for   x<-3/2 u have   |2x+3|=-(2x+3)  & |x-4|= -(x-4)
-3/2<=x<4             |2x+3|= (2x+3)  & |x-4|= -(x-4)
      x>=4            |2x+3|= (2x+3)  & |x-4|=  (x-4)

now i believe u can recombine the above in specified interval to get f(x)

 

[himanshu121]

For problem 1 \frac{df(x)}{dx}= 0 \text{ as the tangent is horizontal say at point x=t}

u will get Quadratic Equation find the roots to 3 decimal place

 

[himanshu121]

For the problem 6 find -dx/dy which will be the slope of the normal

For problem 7

Apply the formula \frac{d (\frac{u}{v})}{dx}=\frac{ v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}
here u and v are u=cosx and v= sqrt(2x-3)

 

[hodeez]

Originally posted by himanshu121
For the problem 6 find -dx/dy which will be the slope of the normal

For problem 7

Apply the formula \frac{d (\frac{u}{v})}{dx}=\frac{ v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}
here u and v are u=cosx and v= sqrt(2x-3)

from what I am understanding, (6) you want me to find the reciprocal negative of the derivative of the original equation? OR find the implicit differentiation and then plugging in the (2,1)

(7) = seems like the division rule, how did i ever miss that? [zz)]

thanks for the replies, I am going to look more indepth into the answers you gave me.

 

[himanshu121]

Giving Hints for long problem

lim(x->3)f(x)=f(3)
i.e f(3-h)=f(3+h) for h->0 and h>0

and f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}
u can substitute x= 4 here and so on

 

[hodeez]

Originally posted by himanshu121
For problem 1 \frac{df(x)}{dx}= 0 \text{ as the tangent is horizontal say at point x=t}

u will get Quadratic Equation find the roots to 3 decimal place

DOH! another simple one over looked

 

[himanshu121]

I must say all are simple

from what I am understanding, (6) you want me to find the reciprocal negative of the derivative of the original equation? OR find the implicit differentiation and then plugging in the (2,1)

u can do it either way

 

[hodeez]

Originally posted by himanshu121
Giving Hints for long problem

lim(x->3)f(x)=f(3)
i.e f(3-h)=f(3+h) for h->0 and h>0

and f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}
u can substitute x= 4 here and so on

im quite consfused on the way you are approaching it. I am thinking, if its continuous the 1st piece must match the 2nd piece @ 3 and then i set it up for k/3+2=k-3-1 and then solved for k which = -9 , then the slope must equal so I am finding the deriv of both pieces and then trying to make them equal again.

 

[hodeez]

May you check this (#9):

y'' = -3(sin^2(x))*(cos^2(x))
and then plug in pi/6 = 180/6 = 30, yes?

 

[himanshu121]

For long problem 2

Take the first hiker along x-axis and other at an angle of 35 deg
After time t its(1 hiker)coordinate will be(2.25t,0) and for second hiker it would be (3.8cos35 t,3.8sin35 t}.

Now apply the distance formula and and differentiate it to get ur answer substitute for t=5.4/2.25

Also it could have been done easily be relative velocity concept but i feel that u have to give Calculus exam right

 

[himanshu121]

may i know how u reach at y'' = -3(sin^2(x))*(cos^2(x))

it is incorrect Pls show me ur steps
though pi/6=30 is correct

 

[hodeez]

Originally posted by himanshu121
may i know how u reach at y'' = -3(sin^2(x))*(cos^2(x))

it is incorrect Pls show me ur steps
though pi/6=30 is correct

y'= 3(sin(x))(cos(x))
y''= 3 * product rule (sin(x))(cos(x))
= 3 * (sin(x))*(-sin(x))+(cos(x))(cos(x))
= -3(sin^2(x))*(cos^2(x))

 

[himanshu121]

look
y=sin^3x \Rightarrow y'=3sin^2x (cosx)

u got y' wrong in ur reply

 

[hodeez]

Originally posted by himanshu121
For long problem 2

Take the first hiker along x-axis and other at an angle of 35 deg
After time t its(1 hiker)coordinate will be(2.25t,0) and for second hiker it would be (3.8cos35 t,3.8sin35 t}.

Now apply the distance formula and and differentiate it to get ur answer substitute for t=5.4/2.25

Also it could have been done easily be relative velocity concept but i feel that u have to give Calculus exam right

is the answer 56.52 rounded?

I used the Cosine Formula for triangles.

Also, I am interested in hearing your relative velocity concept. =)

 

[hodeez]

Originally posted by himanshu121
look
y=sin^3x \Rightarrow y'=3sin^2x (cosx)

u got y' wrong in ur reply

wow, that would have caused havok on the final

 

[himanshu121]

Again how u reached the answer for hiker prob it is incorrect

 

[hodeez]

The method, I'm sure is correct, because that is the method we were taught to use. But my mechanics are probably incorrect. I'm using the Google calculator as I don't have my graphing calculator right now.

 

[himanshu121]

Yup i know the method using the cosine formula is correct u need to recheck ur steps u might be making small errors in calulating

cos35 = \frac{(2.25t)^2+(3.8t)^2-x^2}{2*2.25*3.8 t^2}

After little rearrangement

x^2=5.495000043t^2
so u will get x=2.344141643t

 

[hodeez]

Originally posted by himanshu121
Yup i know the method using the cosine formula is correct u need to recheck ur steps u might be making small errors in calulating

cos35 = \frac{(2.25t)^2+(3.8t)^2-x^2}{2*2.25*3.8 t^2}

After little rearrangement

x^2=5.495000043t^2
so u will get x=2.344141643t

My formula is C= A^2+B^2-cos(c)*A*B
Is that the correct form?

But 2.344 seems too way out of proportional

 

[himanshu121]

u have again quoted the wrong formula the formula which i have quoted previously is authentic

 

[hodeez]

Originally posted by hodeez
My formula is C= A^2+B^2-cos(c)*A*B
Is that the correct form?

But 2.344 seems too way out of proportional

I see my error, I forgot to square the C and derive it, so then I would have to divide the right side by C... Gotta run to the store for my co-workers, so I'll be right back to figure that out

 

[himanshu121]

your are missing a factor of 2 also
Visit for formula

:http://mathworld.wolfram.com/LawofCosines.html

 

[hodeez]

hope i got this

 

[hodeez]

OH NO! the 2!

 

[hodeez]

ugh, i think i understand the concept, so let's recede back to the short answers!

 

[himanshu121]

Originally posted by hodeez
OH NO! the 2!

As far it goes I analyze you , Ur concepts seems to be Ok But your calmness and correctiveness to do a problem is absent u are just making mistakes in formula or small mistakes which are turning out otherwise.

I Advice u to remember the formula(s)with proper definition and Pls do and apply the formula with extreme care.I believe a lot of practice with these problems will help u to get good grade/marks

 

[himanshu121]

Before leaving i give u another advice
The besy way to improve with these kind of a non conceptual errors
is to note down the errors which u have make and then try not to repeat those error

 

[hodeez]

No worries, I usually achieve 90+ marks and the first one to leave the classroom/finish the test. I hate checking =_=

 

[hodeez]

Can't seem to solve Long problems #1.

All I got was a) which is K=9(?) to make it continuous. But to use the H method for B got me all confused!

 

[himanshu121]

f'(4)=\lim_{h\rightarrow 0}\frac{f(4+h)-f(4)}{h}

f'(4)=\lim_{h\rightarrow 0}\frac{\frac{9}{4+h}-\frac{9}{4}}{h}
f'(4)=\lim_{h\rightarrow 0}-\frac{9h}{4h(4+h)}

so f'(4)=-9/16

 

[hodeez]

thanks himanshu, but i seem to have got it in school, before i got a chance to see your answer. Even so, the problem was logically incorrect ( f'(4) was suppose to be f'(3)). I should be 85+ for my finals. thanks.