Category: Differential Calculus, Algebra
"Published in Newark, California, USA"
Evaluate
Solution:
To get the value of a given function, let's substitute the value of n to the above equation, we have
Since
the answer is ∞/∞, then it is an Indeterminate Form which is not
accepted as a final answer in Mathematics. We have to do something first
in the given equation so that the final answer will be a real number,
rational, or irrational number.
Method 1:
Since the answer is Indeterminate Form, then we have to divide both sides of the fraction by a term with the highest degree which is n3 and simplify the given equation as follows
Substitute the value of n to the above equation, we have
Therefore,
Method 2:
Another
method of solving Indeterminate Form is by using L'Hopital's Rule. This
is the better method especially if the rational functions cannot be
factored. L'Hopitals Rule is applicable if the Indeterminate Form is
either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given
function by taking the derivative of numerator and denominator with
respect to n as follows
Substitute the value of n to the above equation, we have
Therefore,
This website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life. This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Monday, June 23, 2014
Sunday, June 22, 2014
Indeterminate Form, Infinity Over Infinity, 2
Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Evaluate
Solution:
To get the value of a given function, let's substitute the value of n to the above equation, we have
Since the answer is -∞/∞, then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We have to do something first in the given equation so that the final answer will be a real number, rational, or irrational number.
Method 1:
Since the answer is Indeterminate Form, then we have to divide both sides of the fraction by 2n and simplify the given equation as follows
Substitute the value of n to the above equation, we have
Therefore,
Method 2:
Another method of solving Indeterminate Form is by using L'Hopital's Rule. This is the better method especially if the rational functions cannot be factored. L'Hopitals Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given function by taking the derivative of numerator and denominator with respect to n as follows
Again, apply the L'Hopital's Rule to the above equation, we have
Since the resulting equation is the same as the given equation, then we cannot use the L'Hopital's Rule because of the repetitive solutions and results. There's no end in this process. In this case, we have to consider the Method 1 in solving the given limits.
"Published in Vacaville, California, USA"
Evaluate
Solution:
To get the value of a given function, let's substitute the value of n to the above equation, we have
Since the answer is -∞/∞, then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We have to do something first in the given equation so that the final answer will be a real number, rational, or irrational number.
Method 1:
Since the answer is Indeterminate Form, then we have to divide both sides of the fraction by 2n and simplify the given equation as follows
Substitute the value of n to the above equation, we have
Therefore,
Method 2:
Another method of solving Indeterminate Form is by using L'Hopital's Rule. This is the better method especially if the rational functions cannot be factored. L'Hopitals Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given function by taking the derivative of numerator and denominator with respect to n as follows
Again, apply the L'Hopital's Rule to the above equation, we have
Since the resulting equation is the same as the given equation, then we cannot use the L'Hopital's Rule because of the repetitive solutions and results. There's no end in this process. In this case, we have to consider the Method 1 in solving the given limits.
Saturday, June 21, 2014
Indeterminate Form, Zero Over Zero, 5
Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Evaluate:
Solution:
To get the value of a given function, let's substitute the value of x to the above equation, we have
Since the answer is 0/0, then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We have to do something first in the given equation so that the final answer will be a real number, rational, or irrational number.
Method 1:
Since the answer is Indeterminate Form, then we have to inspect the given function, factor, and then simplify if possible as follows
Substitute the value of x to the above equation, we have
Therefore,
Method 2:
Another method of solving Indeterminate Form is by using L'Hopital's Rule. This is the better method especially if the rational functions cannot be factored. L'Hopitals Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given function by taking the derivative of numerator and denominator with respect to x as follows
Substitute the value of x to the above equation, we have
Therefore,
"Published in Vacaville, California, USA"
Evaluate:
Solution:
To get the value of a given function, let's substitute the value of x to the above equation, we have
Since the answer is 0/0, then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We have to do something first in the given equation so that the final answer will be a real number, rational, or irrational number.
Method 1:
Since the answer is Indeterminate Form, then we have to inspect the given function, factor, and then simplify if possible as follows
Substitute the value of x to the above equation, we have
Therefore,
Method 2:
Another method of solving Indeterminate Form is by using L'Hopital's Rule. This is the better method especially if the rational functions cannot be factored. L'Hopitals Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given function by taking the derivative of numerator and denominator with respect to x as follows
Substitute the value of x to the above equation, we have
Therefore,
Subscribe to:
Posts (Atom)