Category: Differential Calculus, Trigonometry
"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 apply the double angle formula at the numerator and then simplify 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,
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)
Sunday, June 29, 2014
Saturday, June 28, 2014
Indeterminate Form - Combined, 3
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 (∞ - ∞)/∞ , then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We cannot use the L'Hopital's Rule because the Indeterminate form is (∞ - ∞)/∞. L'Hopital's Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. We have to do something first in the given equation so that the Indeterminate Form becomes 0/0 or ∞/∞.
Since the third degree polynomials in the numerator and denominator have no factors or cannot be factored, then we have to divide both sides of the fraction by the highest degree variable which is x3 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 (∞ - ∞)/∞ , then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We cannot use the L'Hopital's Rule because the Indeterminate form is (∞ - ∞)/∞. L'Hopital's Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. We have to do something first in the given equation so that the Indeterminate Form becomes 0/0 or ∞/∞.
Since the third degree polynomials in the numerator and denominator have no factors or cannot be factored, then we have to divide both sides of the fraction by the highest degree variable which is x3 as follows
Substitute the value of x to the above equation, we have
Therefore,
Friday, June 27, 2014
Indeterminate Form - Zero Over Zero, 7
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 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 factor the numerator and denominator if they can and then simplify 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 Newark, 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 factor the numerator and denominator if they can and then simplify 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,
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