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# Category Archives: Multivariable Calculus

## Total Differential example word problem

Use Differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is 0.04 cm thick.

Solution to this Calculus Differentials practice problem is given in the video below!

## Equation of the Plane Tangent to Surface example problem

Find an equation of the tangent plane to the given surface at the specified point:

Surface z = Point (1, -1, 1)

Solution to this Calculus Tangent Plane practice problem is given in the video below!

## DOUBLE Improper Integral example problem

Investigate convergence or divergence of the Double Improper Integral provided below. Solution to this Calculus Double Improper Integrals practice problem is given in the video below!

## Area of a Circle Formula Proof with Double Integration example question

Use Double Integration to arrive at the formula for the Area of a Circle, A, such that Solution to this Calculus Geometric Formula Proof practice problem is provided in the video below!

## Surface Area of a Right Circular Cone Formula Proof with Double Integration example problem

Use Double Integral to arrive at the formula for the Lateral Surface Area of a Right Circular Cone, SA, such that where r is the radius and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is provided in the video below!

## Area of a Triangle Formula Proof example question

Use Integration techniques in order to derive the formula for the Area of a Triangle, A, such that where b is the base and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Area of a Trapezoid Formula Proof example problem

Use Integration to derive the formula for the Area of a Trapezoid, A, such that where b1 and b2 are bases and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Area of a Circle Formula Proof example

Use Integration to derive the formula for the Area of a Circle, A, such that Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Area of a Circle Formula Proof example question

Use Double Integration to prove the formula for the Area of a Circle, A, such that Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Sphere Formula Proof example problem

Use the Disk Integration method to derive the formula for the Volume of a Sphere, V, such that Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Cone Formula Proof example

Use the Disk Integration method to prove the formula for the Volume of a Right Circular Cone, V, such that where r is the radius and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Torus Formula Proof example question

Use the Washer Integration method to derive the formula for the Volume of a Torus, V, such that where r is the inner (minor) radius and R is the outer (major) radius.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Torus Formula Proof example problem

Use the Shell Integration method to prove the formula for the Volume of a Torus, V, such that where r is the inner (minor) radius and R is the outer (major) radius.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Surface Area of a Cone Formula Proof example

Use Integration to derive the formula for the Lateral Surface Area of a Right Circular Cone, SA, such that where r is the radius and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Surface Area of a Right Circular Cone Formula Proof with Double Integration example problem

Use Double Integrals to derive the formula for the Lateral Surface Area of a Right Circular Cone, SA, where where r is the radius and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is provided in the video below!

## Surface Area of a Sphere Formula Proof example question

Use Integration to prove the formula for the Surface Area of a Sphere, SA, such that Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Torus Formula Proof example

Use the Cylindrical Coordinates (Triple Integration) method to prove the formula for the Volume of a Torus, V, such that where r is the inner (minor) radius and R is the outer (major) radius.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Sphere Formula Proof example question

Use the Spherical Coordinates (Triple Integration) method to derive the formula for the Volume of a Sphere, V, such that Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Cone Formula Proof example problem

Use the Spherical Coordinates (Triple Integration) method to derive the formula for the Volume of a Right Circular Cone, V, such that where r is the radius and h is the height.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!

## Volume of a Torus Formula Proof example

Use the Spherical Coordinates (Triple Integration) method to prove the formula for the Volume of a Torus, V, such that where r is the inner (minor) radius and R is the outer (major) radius.

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!