## 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 *V*_{o }= 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 + … + 2*n* = *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 + … + (4*n *– 1) = *n*(2*n* + 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 + 3^{2} + … + 3^{n – 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:

1^{3} + 2^{3} + 3^{3} + … + *n*^{3} =

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

*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:

*x*^{2} – *y*^{2} + 6*x* + 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* = ±3*x *

(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

25*x*^{2} + 16*y*^{2} + 100*x* – 96*y* = 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 *PF*_{1} + *PF*_{2} = 2** a** directly to find the equation of an ellipse with foci (0, 0) and (4, 0 ) and major axis 2

**= 6.**

*a*

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

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