Jaddybill2
Op deze pagina vind je alle documenten, voordeelbundels en oefenvragen die worden aangeboden door verkoper jaddybill2.
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Limits(rate of change & instanteous velocity)
If f is a function of x, then the instantaneous rate of change at x=a is the limit of the average rate of change over a short interval, as we make that interval smaller and smaller. ... This is the slope of the line tangent to y=f(x) at the point (a,f(a))
- Boek
- College aantekeningen
- • 9 pagina's •
If f is a function of x, then the instantaneous rate of change at x=a is the limit of the average rate of change over a short interval, as we make that interval smaller and smaller. ... This is the slope of the line tangent to y=f(x) at the point (a,f(a))
Limits of functions
A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.
- Boek
- College aantekeningen
- • 8 pagina's •
A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.
Limit laws
The limit of a constant times a function is equal to the constant times the limit of the function. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits. The limit of a constant function is equal to the constant.
- Boek
- College aantekeningen
- • 11 pagina's •
The limit of a constant times a function is equal to the constant times the limit of the function. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits. The limit of a constant function is equal to the constant.
Limits by algebric manipulation and one sided limits
A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1.
- Boek
- College aantekeningen
- • 14 pagina's •
A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1.
Infinite limits
In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero. ... As x approaches 2 from the left, the numerator approaches 5, and the denominator approaches 0 through negative values; hence, the function decreases without bound and .
- Boek
- College aantekeningen
- • 12 pagina's •
In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero. ... As x approaches 2 from the left, the numerator approaches 5, and the denominator approaches 0 through negative values; hence, the function decreases without bound and .
Differentiation
The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
- Boek
- College aantekeningen
- • 10 pagina's •
The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Finding limits by evaluation
Evaluating Limits. Just Put The Value In. The first thing to try is just putting the value of the limit in, and see if it works (in other words substitution). Factors. We can try factoring. Conjugate. Infinite Limits and Rational Functions. L'Hôpital's Rule. Formal Method.
- Boek
- College aantekeningen
- • 9 pagina's •
Evaluating Limits. Just Put The Value In. The first thing to try is just putting the value of the limit in, and see if it works (in other words substitution). Factors. We can try factoring. Conjugate. Infinite Limits and Rational Functions. L'Hôpital's Rule. Formal Method.
Continuity and Discontinuity
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. ... Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.
- Boek
- College aantekeningen
- • 8 pagina's •
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. ... Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.
Limits at infinity and Tangent lines
Limits at infinity are used to describe the behavior of functions as the independent variable increases or decreases without bound. If a function approaches a numerical value L in either of these situations, write. and f( x) is said to have a horizontal asymptote at y = L.) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point...
- Boek
- College aantekeningen
- • 11 pagina's •
Limits at infinity are used to describe the behavior of functions as the independent variable increases or decreases without bound. If a function approaches a numerical value L in either of these situations, write. and f( x) is said to have a horizontal asymptote at y = L.) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point...
Derivative as a function
Learn rules of differentiation and derivatives as a function
- Boek
- Samenvatting
- • 13 pagina's •
Learn rules of differentiation and derivatives as a function