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Surface Area Integration problems

Surface Area of a Solid Integration problem example

Find the Surface Area of a solid generated by revolving the curve

, from    to   , about the x-axis.

 

Solution to this calculus Surface Area of a Solid Integration practice problem is provided in the video below!



 

Arc Length of a Curve Integration problems

Arc Length of a Curve Integration problem example

Find the Arc Length of a curve     , from    to 

 

Solution to this calculus Arc Length of a Curve Integration practice problem is provided in the video below!



 

Area Between Curves Integration problems

Area Between Curves Integration problem example

Find the area bounded by two curves     and 

 

Solution to this calculus Area Between Curves Integration practice problem is provided in the video below!



 

Projectile Motion calculus problems

Projectile Motion In Two Dimensions problem example

An object is launched at angle    from the horizontal with initial speed Vo = 98 meters per second. Determine the time of flight and the horizontal range of the projectile.

 

Solution to this Calculus Projectile Motion practice problem is provided in the video below!



 

Projectile Motion “Baseball Pitcher” example question

A baseball pitcher releases the ball horizontally from a height of 6 feet with an initial velocity of 130 feet per second. Find the height of the ball when it reaches home plate 60 feet away.

 

Solution to this Calculus Projectile Motion practice problem is provided in the video below!



 

Theoretical Projectile Motion example

Show that an object dropped from a height of H feet will hit the ground at time    seconds with impact velocity    feet per second.

 

Solution to this Calculus Projectile Motion practice problem is provided in the video below!



 

Disks Washers Cylindrical Shells Volume of the Solid Integration problems

Volume of the Solid by Revolution DISK Integration Method example

Revolve the region under a curve

on the interval [0, 4] about the x-axis and find the volume of the resulting solid.

 

Solution to this Volume of the Solid by Rotation practice problem is provided in the video below!



Volume of the Solid by Rotation DISK Integration Method example problem

Find the volume of the solid resulting from revolving the region bounded by the lines

 and   

from   to 

about the y-axis.

 

Solution to this Volume of the Solid by Revolution practice problem is provided in the video below!



Volume of the Solid by Revolution WASHER Integration Method example question

Find the volume of the solid resulting from revolving the region bounded by lines

,  and  ,

about the line

 

Solution to this Volume of the Solid by Rotation practice problem is provided in the video below!



Volume of the Solid by Rotation WASHER Integration Method example #2

Find the volume of the solid resulting from revolving the region bounded by lines

,  and  ,

about the x-axis.

 

Solution to this Volume of the Solid by Revolution practice problem is provided in the video below!



Volume of the Solid by Rotation CYLINDRICAL SHELL Integration Method example problem

Revolve the region bounded by the graphs of    and    in the first quadrant about the y-axis using Cylindrical Shells and find the volume of the resulting solid.

 

Solution to this Volume of the Solid by Revolution practice problem is provided in the video below!



Volume of the Solid by Revolution WASHER & SHELL Integration Method example question

Find the volume, using Washer and Cylindrical Shell methods, of the solid formed by revolving the region bounded by curves

  and 

about the line

 

Solution to this Volume of the Solid by Rotation practice problem is provided in the video below!



The Principle of Mathematical Induction problems

The Principle of Mathematical Induction Equality problem example 

Prove the following statement by Mathematical Induction:

2 + 4 + 6 + … + 2n = n(n + 1)

 

Solution to this Mathematical Induction Proof practice problem is provided in the video below!



 

The Principle of Mathematical Induction Equality Proof example question

Prove the following sequence statement by Mathematical Induction:

3 + 7 + 11 + … + (4n – 1) = n(2n + 1)

 

Solution to this Mathematical Induction Proof practice problem is provided in the video below!



 

Exponents & Principle of Mathematical Induction Equality example

Prove the given statement by using Mathematical Induction:

1 + 3 + 32 + … + 3n – 1 =

 

Solution to this Mathematical Induction Proof practice problem is provided in the video below!



 

Exponents & Principle of Mathematical Induction Equality example problem #2

Prove the statement below by Mathematical Induction:

13 + 23 + 33 + … + n3 =

 

Solution to this Mathematical Induction Proof practice problem is provided in the video below!



 

Fractions & Principle of Mathematical Induction Equality example question

Show the given sequence statement holds true by using Mathematical Induction:

 

Solution to this Mathematical Induction Proof practice problem is provided in the video below!



 

Nth Term of Geometric Sequence Formula Proof with Principle of Mathematical Induction

Prove the following formula that finds the Nth term of a Geometric Sequence by using the Principle of

Mathematical Induction:

 

Solution to this Principle of Mathematical Induction Proof practice problem is provided in the video below!



 

EXTENDED Principle of Mathematical Induction Inequality example

Prove the following Square Root sequence inequality statement by using the Extended Principle of

Mathematical Induction:

 

Solution to this Extended Principle of Mathematical Induction Proof practice problem is provided in the video below!



 

Rotation of Axes problems

Angle of Rotation of Axes problem example 

Find an appropriate angle through which to rotate axes to eliminate the xy term in the equation

 

Solution to this Rotation of Axes practice problem is provided in the video below!



 

COORDINATE Equations of Rotation of Axes example question

Find the Transformation Equations to rotate axes through an appropriate angle to eliminate the xy term in the equation

 

Solution to this Rotation of Axes practice problem is provided in the video below!



 

New Axes of Rotation EQUATION example

Find the Equation into which

is transformed when there is rotation of the axes through an appropriate angle to eliminate the xy term in the given equation.

 

Solution to this Rotation of Axes practice problem is provided in the video below!



 

Hyperbola Equation problems

Equation of a Hyperbola problem example

Analyze and sketch Graph of the Hyperbola:

x2y2 + 6x + 34 = 0

 

Solution to this Equation of Hyperbola practice problem is provided in the video below!



 

Equation of Hyperbola ECCENTRICITY example question #2

Find the Eccentricity of the Hyperbola:

 

Solution to this Eccentricity of a Hyperbola practice problem is provided in the video below!



 

Equation of a Hyperbola example #3

Find the equation of a Hyperbola

(a) with vertices (0, ┬▒12) and asymptotes y = ┬▒3x

(b) with foci (3, 6) and (11, 6) and eccentricity

 

Solution to this Equation of Hyperbola practice problem is provided in the video below!



 

Ellipse Equation problems

Equation of an Ellipse problem example

Analyze and Sketch the graph of the Ellipse given by

25x2┬á+ 16y2┬á+ 100x – 96y = 156

 

Solution to this Equation of Ellipse practice problem is provided in the video below!



 

Eccentricity of Ellipse example question #2

Find the Eccentricity for

 

Solution to this Equation of an Ellipse practice problem is provided in the video below!



 

Equation of an Ellipse with Vertices and Eccentricity example #3

Find the equation of an Ellipse with

(a) major vertices (┬▒4, 0) and eccentricity

(b) minor vertices (-3, 4) and (1, 4) and eccentricity

 

Solution to this Equation of Ellipse practice problem is provided in the video below!



 

Equation of Ellipse example problem #4

Use the definition of an ellipse PF1 + PF2 = 2a directly to find the equation of an ellipse with foci (0, 0) and (4, 0 ) and major axis 2a = 6.

 

Solution to this Equation of an Ellipse practice problem is provided in the video below!



 




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