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Category Archives: Multivariable Calculus
Differentials problems
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!
Tangent Plane problems
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 problems
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!
Geometric Formula Proof Double Integral problems
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
where r is the radius.
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!
Geometric Formula PROOF Integration problems
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
where r is the radius.
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
where r is the radius.
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
where r is the radius.
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
where r is the radius.
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
where r is the radius.
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!
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