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glenn101

Member

Registered: 2008-04-02

Posts: 108

Calculus

Hi, I'm just beginning calculus, all we have learned at the moment is limits, finding the derivative (by first principles and by rule not including the chain rule) and antidifferentiation (indefinite integrals) I have 2 questions which I just cannot get, please help!

find:

*indefiniteintegral5x^4+4x^3-2x^2/2x^2 dx

and

Find the equations of the tangent and the normal to the curve with equation y=3x^2-7x+2 at the point where the tangent is parallel to the line with the equation y=2x+5.

Thank you

P.S where can I learn higher level calculus? know of any websites? that just go on from where I finished not start at integrals etc, Thanks!

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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Calculus

now you can use

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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Calculus

Slope of the tangent at any point to the given curve is given by

while the slope of the given line segment y=2x+5 is 2. For the tangent to be parallel to the given line, their slopes must be equal.
Hence, 6x-7=2 which gives x=3/2. Putting this in the equation of the curve, we get y=-7/4.
Hence, equation of the required tangent is the equation of a line passing through (3/2,-7/2) and with slope 2.
i.e. y=2x-19/4 and the equation of the normal is the line passing through the same point with slope -1/2 i.e. 2y=-x-1 !

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If two or more thoughts intersect, there has to be a point!

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Calculus

Last line corrected: i.e. (y - (-7/4))= 2(x - (3/2)), and this is y + 1.75 = 2x - 3, and that's y = 2x - 4.75, so that's your tangent line that goes thru (1.5, -1.75). 
And the normal line is perpendicular, slope is not 2, but -1/2, just flip it over and negate it.
So y - (-1.75) = (-1/2)(x - 1.5), that's my favorite line equation, you just put the points in the subtractions.
And that's also y + 1.75 = -0.5x + 0.75 and that's y = -0.5x - 1, so that's your normal.

(Just a silly error at the end he made, he had -7/4, but changed it to -7/2 by mistake)

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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Calculus

Oh!
I don't know why i keep on making such silly mistakes??

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If two or more thoughts intersect, there has to be a point!

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Calculus

Thanks alot guys:D
Any ideas where I can learn higher calculus though? I'm interested in calculus:)

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"If your going through hell, keep going."