Geometry Problems..

[oman]

1. the base of a solid is the region in the xy plane bounded by the

parabolas y=x^2 ans x=^y2. find the volume of the solid if every cross

section perpendicular to the x-axis is a square with its base in the

xy plane.

 

2. given y=x^5 - 4x^3 + 5x

a. locate the exact or approximate intercepts

b. identify any axis of symmetry

c. determine the curves behavior at positive and negative infinity

d. use the first and second derivative to locate turning points

 

3. find the area common to r=1+cos@ and r=3^(1/2) sin@

 

4. specify the points of intersection of rcos@=1 and r=4cos@

 

5. tnagents are drawn to the ellipse x^2/a^2 + y^2/b^2 =1 and the

circle x^2 + y^2 = a^2 at points having the same abscissa. prove that

these tangents cross OX (a-axis) at the same point.

 

6. find the volume generated by rotating the region bounded by

(x-1)^2 + (y-2)^2 = 4 around

a. x axis

b. y -axis

c. x = 3

d. y = 4

 

[Difficulty]

I need help in one and five a lot!!

[Country Boy]

1. the base of a solid is the region in the xy plane bounded by the

parabolas y=x^2 ans x=^y2. find the volume of the solid if every cross

section perpendicular to the x-axis is a square with its base in the

xy plane.

So "thin slab" perpendicular to the x-axis would be a square with base running from y= x^2 to x= y^2 (y= sqrt(x)). It's "thickness" would be dx so it would have volume x^2(sqrt(x))dx. To find the volume of the whole figure, integrate that with x going from 0 to 1. Do you see why x is from 0 to 1?

 

2. given y=x^5 - 4x^3 + 5x

a. locate the exact or approximate intercepts

b. identify any axis of symmetry

c. determine the curves behavior at positive and negative infinity

d. use the first and second derivative to locate turning points

 

3. find the area common to r=1+cos@ and r=3^(1/2) sin@

 

4. specify the points of intersection of rcos@=1 and r=4cos@

 

5. tnagents are drawn to the ellipse x^2/a^2 + y^2/b^2 =1 and the

circle x^2 + y^2 = a^2 at points having the same abscissa. prove that

these tangents cross OX (a-axis) at the same point.

Differentiating x^2/a^2+ y^2/b^2= 1 with respect to x gives 2x/a^2+ 2y/b^2 y'= 0 so y'= -b^2x/a^2. Differentiating x^2+ y^2= a^2 with repspect to x gives 2x+ 2y y'=0 so y'= -x/y.

 

6. find the volume generated by rotating the region bounded by

(x-1)^2 + (y-2)^2 = 4 around

a. x axis

b. y -axis

c. x = 3

d. y = 4

 

[Difficulty]

I need help in one and five a lot!!

[oman]

thankx a lot!! GOD Bless you..

 

guys, i still need help. thanx in advance..

 

anyone, pls help me. in 2, 3, 4 and 5. just help me in setting the equation, i will then solve it. i little confused in integral especially in number 3 and 6. thank a lot, i hope you guys will help me.